Hold on: you’re entitled to your own opinion on this character, of course, but these things didn’t happen in a vacuum. Let’s back up and consider the context and Jake’s perspective:
Throughout the second movie, Jake's primary goal, by his own words, is protecting his family: "a father protects. It's what gives him meaning". That is, therefore, the lens through which his actions must be viewed.
He's also experienced with the ins and outs of war. Remember, this guy was already a paralyzed veteran before he ever even set foot on Pandora. He is intimately familiar with the mortal dangers involved in war, and understandably doesn't want his kids anywhere near it.
When he gets frustrated with his sons for disobeying him, it's not merely a "ugh you didn't do what I said". It's "you didn't do what I said and because of that you put yourself and those around you in real and serious danger".
When Jake allows Neteyam and Lo'ak to participate in the train raid, he instructs them to keep their distance and act as spotters. Lo'ak disobeys...and as a result Neteyam gets injured.
Jake instructs his kids to stay away from the old battle ground. Lo'ak, Kiri, and Tuk disobey...and get kidnapped by the recoms, having to be rescued from a rain of bullets and barely escaping with their lives.
Jake instructs Neteyam to stay back while he and Neytiri go rescue the other kids from the recoms. Neteyam disobeys...and would've been shot much earlier in the film had Jake not been there to tackle him.
Once they arrive at the Metkayina, Jake implores the kids to be on their best behavior and stay out of trouble: he doesn't want to tread on the clan's hospitality by causing a scene. Remember how I said Jake's primary goal throughout the film is protecting his family? This is an offshoot of that: right now he believes that the best way to keep his family safe is to take refuge with the Metkayina. Ronal was already skeptical about letting them stay; Jake finds it best to make sure everyone keeps their heads down and not cause trouble lest she and Tonowari might change their minds and ask them to leave. Staying on the chief's good side is important to that goal.
....and then Lo'ak and Neteyam get into a fistfight with the chief's son. While their motivations may have been noble (defending Kiri), you can understand why this is conflicting for Jake.
When Lo'ak defends Payakan to Ronal and Tonowari, although what his is saying is true, he is very clearly upsetting the tsahìk and olo'eyktan of the clan, who are furious. Neytiri is actually the first to warn him that he's speaking out of line:
...and it's only after Lo'ak persists with talking back to Tonowari despite his mother's warning that Jake steps in and puts a stop to it for the sake of making peace with the chief.
"You bring shame to this family" was a different scene; it came before this one, right after Lo'ak returns to the village after meeting Payakan for the first time.
In that scene, the whole village had been searching for Lo'ak after Aonung bragged to Neteyam about abandoning Lo'ak outside the reef, and Neteyam immediately went to report to Jake. When Lo'ak is found, Jake runs up to make sure he's ok, and after it's clear that Lo'ak is safe, Jake doesn't yell or lecture; he's just relieved and it seems that he just wants to go home. At this point, as far as Jake is aware, Lo'ak was cruelly taken advantage of by the local kids and left in a dangerous situation, but is now home safe. Which is pretty close to the truth.
...but then when Tonowari (rightfully) declares Aonung's blame for the incident, Lo'ak speaks up to take the blame himself, claiming that going beyond the reef was all his idea which Aonung had tried to talk him out of.
We the audience know the true story of course, we know that the incident was absolutely Aonung's fault at not Lo'ak's, and we know that Lo'ak really was just trying to do what Jake asked and make friends with the reef boys. But the thing is, Jake doesn't know that. As far as Jake is aware, based on what Lo'ak himself had just admitted, the situation has suddenly shifted from "my son got taken advantage of by the local bullies" to "my son purposefully and of his own free will went out to a place that he knew was off-limits and dragged the chief's son and a few others along with him despite them trying to talk him out of it, thus putting not only his own life (which would be bad enough on its own) but also Aonung+friends' lives in danger".
That's why he's so mad. Lo'ak does not have a reputation for lying, but he does have a reputation for struggling to follow orders and going places he's not supposed to (for example, the old battleground earlier int he movie). So for better or for worse, when Lo'ak speaks up to take the blame for Aonung, Jake has zero reason not to believe this version of events, even if we the viewers know that it's inaccurate.
Speaking of taking blame, Jake tells Neteyam to "stop taking the heat for this knucklehead" because Neteyam does try to take responsibility for Lo'ak's dumb decisions a lot and Jake knows this. In this particular instance, Lo'ak is the one to threw the first punch; if he'd just let it go and walked away after Neteyam warned Aonung to leave Kiri alone, things would've been fine and the issue would've been avoided. It's not at all wrong to recognize "no, Neteyam, you didn't start this, I know you didn't start this, Lo'ak needs to take responsibility for his own impulsive actions".
As for "you've done enough", I do agree that that's the worst one, and that it'd be best for Jake to apologize to Lo'ak for it if he hasn't already. However, again, let's look at the context.
Neteyam has just died. Like, less than five minutes ago. His body isn't even cold yet. Jake's mind is still reeling, he's devastated. His goal throughout the movie has been to keep his family safe, to keep his kids away from the war...and now, his worst nightmare has just come true: the war has taken one of his children away from him. His beloved firstborn son just bled out in his arms. He just watched his baby boy take his last rattling breath, he watched the light leave his eyes as his last words died in his throat.
But the battle isn't over yet. Kiri and Tuk are still being held hostage by the recoms. Jake has no choice but to go after them. Lo'ak asks to come, but of course Jake doesn't want Lo'ak to come. He already lost one of his sons today, why in the ever-loving heck diggity would he be willing to risk losing the other? Why would he want to bring his other son right back into the danger zone, especially the son who's proven time and time and time again that he struggles to follow orders and ends up in greater danger because of it?
"Lo'ak already blames himself because he's the one who insisted on going back to save Spider" that may be true, but how in the world is Jake supposed to know that at this point? He wasn't there to see that conversation; he was busy fighting somewhere else.
Jake's "you've done enough" has little (if anything) to do with blaming Lo'ak for Neteyam's death and much more to do with "please for the love of all things decent stay out of the way where you can't get yourself or anyone else hurt, for your own sake".
Did he say it poorly, yes absolutely, and I can see why Lo'ak could interpret as blame even if Jake didn't mean it that way, and yes, that sucks, absolutely. But goodness gracious, Jake was not thinking particularly clearly or rationally in this scene. He was exhausted, he was in shock, he was devastated, he was mourning, and he was still terrified for the rest of his family. Saying one poorly-worded insensitive thing like this in a moment of intense emotional suffering does not an "abuser" make.
Jake is not a perfect person. He makes mistakes, as everyone does. But he's not cruel or abusive, and boy howdy he's trying. He's flawed but he's doing the best he can given the circumstances. His strictness stems from fear and his fear stems from love.
I suppose I cannot force you to view Jake as a good dad—as I said at the beginning, you're entitled to your own opinion—but I hope that if nothing else this at least helps you understand his perspective and why he does the things that he does 🙂
If you (or anyone else reading this) would like an even more in-depth exploration of Jake's perspective throughout the entire movie and why I think he's a good dad, you can check out my absolute beast of a post here (warning, it's long lol). Eywa ngahu!
