Im glad that we can agree on what the film is saying in these scenes, and perhaps I can go from there and explain why I have issues with self-interested Objectivist Superman. For the record, I feel comfortable calling him Objectivist because of a number of factors, including but not limited to the directors own beliefs and previous films, the adapted source material, and Batman being similarly ego-driven and self-interested. So, leaving aside my personal issues with Objectivism as a philosophy, let me get just a little into why I dont like this version of self-interested Superman.
A quick note: I do think being motivated to act selflessly out of self-interest to be the same thing as acting in one's self-interest. Sure, its nice for other people, but selfless action rooted in self-interest is subject to change depending on the subjects self-interest. For example, Superman might be motivated by self-interest to help everyone, but if helping other people got in the way of his self-interest, say by causing him to suffer through losing a loved, he would no longer be interested in helping everyone. A truly selfless person would push through that and do the right thing no matter what is in their personal interest. It might seem pedantic, but I think its an important distinction to make.
As you noted, lots of Superman stories are interested in selflessness vs. self-interest. The original Richard Donner film ends with Lois Lane dying in his arms after he chooses to stop the other missile from destroying the West Coast. Of course, he proceeds to turn back time and save her too, which I think is an issue with the film, but hes Superman, cutting the Gordian knot is what he does. The second Donner film hammers this point home even further, with Superman foregoing a normal relationship with Lois to stop Zod and crew from conquering the world. All-Star Superman flies into the sun to keep it from exploding, Red Sun Superman ends up sacrificing himself in space after realizing the negative impact hes had on humanity, etc. A lot of my favorite Superman stories end with a self-sacrifice or loss on Supermans part to reflect the responsibility in doing good for goods sake.
This isnt necessarily an issue; I think its completely possible to have a Superman story work where Superman ends up acting in his self-interest and gives himself a happy ending (Whatever Happened to the Man of Tomorrow? comes to mind). The problem with BvS Superman is that if
this Superman (a Superman willing to kill for starters) is motivated more by self-interest than selflessness, then that means
Batman and Lex are right. A Superman that isnt preternaturally driven to help people, no matter the cost, is a ticking time bomb that needs to be disarmed. Supermans arc, especially with regard to the advice he gets from his parents, his loose morality when it comes to the safety of people close to him, his frustration and distanced demeanor in the times he does save people, etc., doesnt end up refuting that idea. Again, thats not necessarily a flaw with the film; a film where mere mortals task themselves with putting down an unstable god could be interesting if done well.
The problem is that the film wants us to believe at the end that Batman and Lex were somehow wrong, that Superman was a hero of the people, a beloved martyr. Im sorry, but the Superman I saw, the one who was driven to attempted-murder (and actual murder in the case of the terrorist dude) over his loved ones, the one who at best wouldnt give a shit if he didnt have his loved ones and at worst would become a tyrannical despot, isnt that. A self-interested Superman who only happens to help others because it suits his self-interest isn't the kind of hero I'd be comfortable memorializing. If I was Batman I would be relieved that Doomsday and Superman managed to kill each other (which is another issue with the film, albeit not as central), not in mourning. The issue is mostly side-stepped by his death at the hands of Doomsday, because the question of What do we do about Superman? is moot now that hes dead, but it feels unearned to end your film one way when you spend the majority of your time depicting him as the opposite.
EDIT: Sorry for all the lightning edits, I'm a bit of a perfectionist when it comes to my long-winded posts