Kakashi deferring to Sasuke as squad leader is one of Kakashi's better moments with Sasuke. Kakashi handled this situation tactfully, and it's pretty much the only time Kakashi evokes a positive reaction from Sasuke in all of Shippuden. The only other thing Kakashi had done that evoked a positive reaction from Sasuke was his apology to Sakura, and that wasn't even to Sasuke.

Rather than lecture Sasuke, this time Kakashi uses tact and responds to the feedback he is getting from Sasuke and adjusts accordingly.

Conflict between the team arose when Sakura inquired what was outside of Sasuke's Susano'o and Sasuke snapped at her to be quiet under the pretense that she wouldn't be able to do anything anyway.

It is Kakashi's deference that earns Kakashi's points with Sasuke here. And it was the same in the Land of Iron, since Kakashi's apology to Sakura was a deferential gesture, not an assertive, dominating one.

It's interesting, since typically, Sasuke rewards pushiness and persistence and tends to reward assertive people more than complaint ones. People don't usually win points with Sasuke by backing down, but by pushing him, which is what we see in his interaction with characters such as Naruto, Sakura, Gaara, Sai, Boruto, and Sarada (Karin is the one exception; persistence and pushiness worked against her rather than for her). Persistence and pushiness with Sasuke in dialogue pays off more than giving up, even when Sasuke adversely tells them to get lost. Sasuke respects and rewards pushiness and conversely doesn't respect people who give up easily. Be pushy with Sasuke and they'll get somewhere; give up and he won't give them anything.

But evidently the rules are a bit different for Kakashi. Kakashi backs down, yet it works better than being pushy does.

Sasuke has clammed up and selfishly monopolizes intel on what lies outside the Susano'o, prohibiting Team 7 from knowing what the present situation is. Team 7 attempts to get Sasuke to reveal what has happened outside the refuge of the Susano'o wings, but Sasuke refuses all three of them, degrading Sakura and Kakashi both as useless, and he dismisses all three of them as incapable of concocting a strategy to defeat Madara. Instead of sharing information so the quartet can formulate a strategy, Sasuke hoards the information to himself. His lifestyle has led to him becoming a loner, and even at the best of times, Sasuke has never been good with freely sharing information, as he is generally secretive and closed off, preferring to keep things close to the chest.

All of Team 7 protest Sasuke's silence, observing that they need to come up with a strategy together, and they can't do that when Sasuke is withholding critical information from them. However, Kakashi's decision to defer to Sasuke succeeds where Sakura's gentle probing and Naruto's angry scolding fail.

Naturally both Naruto and Kakashi are incensed by Sasuke's treatment of Sakura when he coldly shuts her down by refusing to answer her question. For once Kakashi stands up for Sakura, letting Sasuke know that he doesn't appreciate the way Sasuke is treating Sakura, but in a clever way designed to reprimand Sasuke while also emphasizing and teaching teamwork (yes, Kakashi is finally teaching teamwork here). Kakashi defends Sakura by noting that Sakura is merely giving voice to what both he and Naruto are both already thinking, since they want to know what is happening outside too.

Kakashi explains how teamwork works: teams share information so that they can concoct a strategy to take on the enemy together. The more minds to brainstorm and strategize to come up with a plan, the better. Particularly since it's not like Sasuke would be fully aware of his team's abilities at this point, nor they his, seeing as how the team has been apart for 4 years and their arsenals have changed during that time.

Kakashi remains impressively calm during this conversation. Sasuke is rude to Sakura, then he directs that rudeness at Kakashi the moment Kakashi tries to stand up for Sakura. Though irritated by Sasuke's savagely blunt manner, Kakashi doesn't let that rile him up, but instead remains calm and pragmatic.

Sasuke has essentially been a loner for the past 4 years, and Kakashi seems to take this into consideration. Sasuke is likely not accustomed to giving away intel, as he's used to being only in charge of himself. So Kakashi appeals to Sasuke's logical side by pointing out the pragmatic value of sharing information with Team 7. Strategically, it only makes sense to inform Kakashi, Sakura, and Naruto of what is transpiring outside, since they are all fighting a common enemy. It's a waste of time and resources to idly stand around. Sasuke sharing information of what is transpiring outside gives all four of them a chance to come up with a strategy. At the very least it will brace them for the threat that awaits them outside. If Sasuke wants to defeat Madara, it is only logical that he should tell Team 7 about what's outside.

It's another lecture, but one gently and tactfully given, unlike Kakashi's lectures in the past. Kakashi isn't lording some ideal over Sasuke; he's merely asking for cooperation.

Even so, Sasuke coldly shuts down Kakashi, not wanting to hear another reprimand and lecture, of which Sasuke has had enough of from Kakashi. Sasuke makes it clear he thinks Kakashi is just as useless and extraneous as Sakura and has nothing to contribute to winning the war. At this point, Sasuke believes the only person still of use to him in the current situation is Naruto. Everyone else is too impotent, weak, or exhausted to have anything worthwhile to contribute.

Despite Kakashi's request that Sasuke share information with the team, Sasuke continues to hold on to his monopoly of information, which puts him in a place of control and authority. Sasuke is presumptuous enough to self-appoint himself in command by saying that he'll direct, and that Kakashi should "be quiet for a bit". Which is the polite (sort of) way of telling Kakashi to shut up.

To be fair, Sasuke isn't even saying that Kakashi and Sakura are useless per se, just that they are useless right now, for the moment. And Sasuke was correct in his assessment that none of them could do anything for the present. Likely that's as far as his meaning extends: they can't do anything about it, so knowing anything won't change anything. 

Naruto jumps in to protest Sasuke's decision, berating Sasuke for not being a team player. But instead of siding with Naruto and likewise protesting Sasuke's decision to hoard information from the team, Kakashi makes an interesting move by instead siding with Sasuke, agreeing Sasuke is right. Kakashi admits he's useless at this point. He is tired, wounded, depleted of chakra and has lost his Sharingan, the most defining ability Kakashi had relied on for approximately 20 years. Without it, Kakashi admits he's of little help.

Then Kakashi takes it a step further by acknowledging that Sasuke's abilities make Sasuke the most useful in the present situation. Since Sasuke is the only one who knows what's going on and is most informed, Kakashi decides that Sasuke should be the team leader for the time being.

It's a kind and generous decision, since Sasuke is hoarding information and leaving Team 7 little choice but to comply with his leadership. Presumably they can't willingly leave the shelter of his Susano'o, and they have zero knowledge of what threats await them should they step outside.

But instead of complaining about Sasuke's dictatorial decision to assume the role of leader, fighting against Sasuke's selfish decision, or even pointing out how his hoarding information is illogical, impractical, and unwise, Kakashi instead makes the decision to comply with it and support Sasuke appointing himself squad leader.

In doing so, Kakashi is actually, for a rare change of pace, modeling teamwork. Kakashi isn't just hypocritically lecturing how people should do teamwork while not doing anything of the sort himself. Kakashi is still preaching teamwork, but this time he's modeling it too. Kakashi is modeling trust, because if Kakashi doesn't trust Sasuke, then he can't expect Sasuke to ever trust Kakashi or Team 7 either. Kakashi is already completely dependent upon Sasuke's Susano'o protection, but instead of pushing angrily against Sasuke withholding critical intel from him (and he would be justified to do so) and for forcing Team 7 to be completely reliant on Sasuke's leadership, Kakashi calmly accepts it and complies with it, making a decision to follow Sasuke's lead even though Kakashi doesn't have to do so.

It's a gracious move, since Sasuke hasn't done much to earn Team 7's trust, and his unwillingness to reveal his motivations is suspicious and makes him of most dubious character. Yet in spite of all that and in spite of Sasuke's condescending attitude, Kakashi decides to defer to Sasuke's leadership, recognizing that Sasuke's abilities outclass his own in this situation. If Sasuke is unwilling to share information, then there is nothing Kakashi can do in the present situation until Sasuke decides to lower his Susano'o.

And Sasuke responds very well to this. Kakashi's words capture Sasuke's interest. Sasuke is pleased at Kakashi appointing him as team leader, as he responds positively by reversing his decision to withhold information from Team 7. Because of Kakashi deferring to his leadership, Sasuke finally relinquishes the information that Team 7 had been demanding from him: the Infinite Tsukuyomi has been activated, and he thinks that Team 7 are the only humans not under the world-wide genjutsu.

Perhaps it is because Kakashi is finally acknowledging Sasuke's abilities and that Kakashi is no longer treating Sasuke like a kid but is treating him like an adult and an equal. Kakashi is no longer talking down to Sasuke; rather, Kakashi is respecting Sasuke's decisions and judgement and choosing to follow them.

Anyway, this exchange reinforces the idea that Sasuke has been seeking approval and acknowledgement from Kakashi all this time, because when he gets it, Sasuke is receptive to it and gives Kakashi what he wants. Kakashi is no longer acting like Sasuke's boss or squad leader. In fact, Kakashi forgoes his position as squad leader by dubbing Sasuke more qualified for the position, which is evidently exactly the kind of thing Sasuke wanted to hear. In the Land of Iron arc, Sasuke expressed irritation at Kakashi underestimating him and his abilities. So it's natural that conversely, Sasuke responds positively when Kakashi credits Sasuke's abilities and acknowledges them, even going as far as to dub them superior to his own, and that Kakashi is presently useless, particularly in comparison to Sasuke.

Plus rather than discredit, downplay, and dismiss everything Sasuke says, this time Kakashi agrees that Sasuke has a point, and Sasuke is considerably more agreeable when his input isn't immediately disregarded by his ex-sensei. Kakashi is finally taking Sasuke seriously, and so conversely, Sasuke finally takes Kakashi seriously. If Kakashi is going to start treating Sasuke as an equal, then Sasuke reciprocates by treating Kakashi as an equal. Which makes it appear that Sasuke is somewhat mirroring Kakashi's attitude towards him: if Kakashi talks down to Sasuke in a self-righteous "I know everything so do everything I say", then Sasuke mirrors that by likewise treating Kakashi with condescending derision in return.

But when Kakashi takes Sasuke seriously and treats him like a fellow solider, Sasuke takes things seriously and treats Kakashi as a fellow soldier.

Actually, Kakashi goes above and beyond in this regard, because he doesn't just treat Sasuke as an equal, he acknowledges Sasuke as the superior warrior, and he is trusting and relying in Sasuke's leadership and ability to strategize and come up with a plan. No longer is Kakashi treating Sasuke as a subordinate child he can impose his will on; he is treating Sasuke like an equal with the respect of a comrade.

Perhaps this is why Sasuke's demeanor so quickly shifts. Respect and trust aren't things he expected from Kakashi, yet they are things he wants from his ex-sensei, because the instant he gets them, Sasuke immediately complies with Kakashi's request. Kakashi has given Sasuke something he wants (respect and acknowledgement), so Sasuke in turn gives Kakashi something he wants (intel and information).

This becomes another instance of Sasuke focusing on what people are doing, not what they are saying. When Kakashi verbally tells Sasuke to use teamwork and to rely on his team, that accomplishes nothing except Sasuke remains clammed up on sharing info. But when Kakashi shows how to use teamwork by putting his trust in Sasuke and choosing to rely on Sasuke, Sasuke reciprocates by using teamwork as well and telling Team 7 what they need to know to plan for their next move.

Therein lies the folly of all Kakashi's attempts to teach Sasuke before this point: Sasuke doesn't need lectures, he needs someone to model an example for him to follow. When Kakashi finally uses actions and not just words to teach Sasuke, it works much more effectively.