Kakashi telling Sasuke that "times were bad back in my day" sounds out of touch and Kakashi neglects addressing the issues Sasuke is currently struggling with. 

Kakashi acts like everything in the village is normal, unchanged, and safe, when the Leaf Village is currently reeling from a devastating blow to its warrior force and presently short-staffed and vulnerable to enemy attacks. 

Sasuke is still struggling with the grief over his clanmates' deaths and feeling frustrated and helpless with his slow increase in power and personal growth as a ninja. Sasuke's parents are dead, his people are essentially extinct, he's a lone massacre survivor, he has almost died multiple times in the past couple months, one of the most heinous and dangerous criminals in the world is targeting Sasuke with the intent of stealing Sasuke's body, the village leader had been killed and seemingly no one in Konoha is strong enough to defeat Orochimaru, Sasuke doesn't know what the curse mark is or what it's doing to his body and will, his fear of the curse mark taking over him at any given moment, a third of Konoha's fighting force has been exterminated, the village's infrastructure has taken a large hit and needs repairs, Sasuke has been brutally tortured by his own brother and as a result he has recently developed Complex-PTSD (which was formerly "just" PTSD), and his teammate Naruto is being targeted by his very powerful and very dangerous brother who no one in Konoha is strong enough to stop, not to mention the looming existence of a dangerous secret criminal organization at large. Things were bad in Kakashi's day, but things are pretty bad and dire right now too, and Kakashi needs to address these issues more directly than just "let go of revenge and that will solve your problems". Letting go of revenge will solve some problems for Sasuke, but certainly not all of them with things the way they are. 

Kakashi completely neglects addressing the troubling issue of Itachi, which is inevitably going to be troubling to Sasuke, especially since Sasuke suffers from a severe case of survivor's guilt and blames himself for the death of his parents and his clan.

If Sasuke still feels guilty and blames himself for allowing that tragedy to happen, shouldn't we assume that if he cares about Team 7 (and he obviously does), Sasuke might be living under a dark paranoia that the same thing might happen all over again? Unless Sasuke wants to twiddle his thumbs while Itachi wipes out his newfound family all over again, he's going to have to take action to stop Itachi if he wants to protect his team. Waiting around for things to get even worse is anathema to Sasuke. Inaction goes against his core character; Sasuke can't stand to sit around helplessly and do nothing.

Sasuke isn't oblivious to his brother's insane strength. Sasuke knows Itachi is incredibly strong. Their recent reunion only reaffirmed that, making Sasuke wonder if it was a power gap that could ever be bridged.

Even years later in Shippuden, Sasuke doubts if even Orochimaru would be strong enough to defeat Itachi, aware that defeating Itachi would be difficult if not downright impossible.

If Itachi annihilated Sasuke's entire clan, then shouldn't Sasuke assume that Itachi might also annihilate his team one day? Itachi said he was leaving Sasuke alive so that he might be an entertaining challenge to fight one day, so it's reasonable to deduce that Itachi might target Sasuke's loved ones to stoke Sasuke's desire for revenge or even just to sadistically torment Sasuke, something he has already done multiple times. After all, in their most recent encounter (about a month ago, or a few days ago by Sasuke's perception of events), Itachi told Sasuke that he didn't have enough hate. If Itachi cared about Sasuke as a future challenge, he might target Sasuke's teammates to rile Sasuke up and refocus his anger just for the fun of it.

Revenge is bad, and it's clearly very destructive for Sasuke. That said, Itachi does need to be brought to justice and he does need to be dealt with, and with the exception of Sasuke, everyone in Konoha seems concerningly disinterested in bringing Itachi to justice and making him pay for his crimes. Itachi wiped out what was probably several hundred members of Konoha's most elite and prestigious clan, if not several thousand. They were major assets in Konoha's arsenal, meaning that Itachi effectively dealt Konoha's defenses a crippling and devastating blow by eliminating their strongest clan.

There should be a huge outcry against Itachi based on morality alone: Itachi committed genocide of an entire race, leaving only one survivor, and the people of Konoha are just going to take that? Konoha should be enraged and on a relentless hunt for Itachi, tracking Itachi down to kill him for slaughtering their comrades. As long as Itachi runs rampant, what's to say he won't wipe out more innocent villages or clans outside the village? If Konoha had any concern for the greater good, they would hunt down Itachi or search for a way to take him down. 

Kakashi needed to find a way to deal with the problem of Itachi or otherwise offer Sasuke team support in achieving such a goal. Kakashi needed to offer some resolution other than "let's keep allowing a mass-murderer to run lose because one teenager has a bad attitude problem".

Regardless of Itachi's reasoning, Itachi already is targeting Sasuke's teammates: he put Kakashi in a permanent coma and he explained he was targeting Naruto. Sasuke knows full well that Naruto could never stand a chance against his big brother. Itachi destroyed Sasuke's old life; now it appears Itachi intends to destroy Sasuke's new one too.

Yet Kakashi says nothing about this at all and nothing whatsoever about the Itachi treat looming over Team 7. Worries and fears must be assaulting Sasuke's mind about this on at least some level, yet Kakashi does absolutely nothing to assuage or allay these fears. There's no promised precautions about taking Itachi down before he kills Naruto, no extra security measures taken for Naruto's safety, no added security to prevent the Akatsuki from waltzing into Konoha whenever they feel like it. Nothing.

At this point, I'd say Sasuke protecting his team and Sasuke avenging his clan have morphed into the same thing: Itachi has to go if Sasuke doesn't want his teammates to die at his older brother's hands.

But Kakashi oddly treats those matters as entirely disparate, dismissing Itachi as a threat, even though Itachi had just put Konoha's strongest shinobi (after Tsunade, Guy, and Yamato) out of commission for an entire month when the village was already dangerously weakened and vulnerable to enemy attacks.

Furthermore, where's Kakashi's sense of justice? Sasuke never used to misbehave this way until Itachi messed him all up, yet we don't see any internal dialogue of Kakashi getting angry at an abusive older brother bullying and abusing his student and walking all over Sasuke like he owns him, injuring his student and traumatizing the poor kid so badly that it turned Sasuke into an angry and unmanageable jerk when previously Sasuke used to be patient, calm, and mature.

Instead of feeling furious at Itachi for messing with his students or wanting to put an end to Itachi bullying and traumatizing his little brother once and for all, Kakashi instead takes out his annoyance on Sasuke for being so difficult and having a bad attitude, showing total disinterest in bringing Itachi to justice. Even knowing how much Itachi's existence is tormenting Sasuke's mind, Kakashi doesn't see Itachi's presence as an issue. Instead he tells Sasuke to forget about the dangerous S-class criminal no one seems able or willing to stop.

The great danger Sasuke was in when he faced up against Itachi doesn't seem to bother Kakashi either. We don't see any sign of relief that Sasuke survived a second encounter with Itachi, which is nothing short of miraculous considering what Itachi did to every other human bearing the surname Uchiha.

Furthermore, what's to say that Itachi doesn't have some personal vendetta against the Leaf Village? Itachi isn't just a threat to distant villages or whoever might find themselves in Itachi's path of destruction. Itachi could come back to Konoha anytime and wreak havoc if he so wished. We even saw that happen when Itachi returned to Konoha expressing his desire to obtain Naruto Uzumaki, but I guess Konoha isn't particularly concerned about that? And Kakashi is picking now of all times to tell Sasuke he shouldn't bother with taking down Itachi, when a member of Team 7 is Itachi's prime target? At this point it doesn't even matter whether or not Sasuke goes seeking out Itachi, because Itachi is going to eventually come seeking Naruto, and Kakashi is going to have to figure out how to prepare Sasuke for that day, both physically and mentally.