I had a long response that adress each individual fact but it got lost. I'll try the water down version.
I hate it when that happens. Especially when I type up extremely long messages on Gmail with lots data over the course of several hours that end up getting me locked out of my account (yes, Gmail does that frequently due to apparently finding cluttered emails suspicious). You have my sympathies.
Either it is stupid for him to think of Endeveor as a jerk based on what he know, and in this case doing the same with Shouto is stupid or he is right about endeveor and Shouto. Either way his assertion about Shouto has nothing to do with him being Endeveor's son, it's about making the same observation in similar context and getting the same conclusion. If it was Bakougou he saw those eyes in, it would be the same. It might be stupid but it's not bias.
It's not dumb of him to think that Endeavor's a jerk. I can't even blame him for having a negative impression of a guy who's first response to him is "get out of my way" in Shouto. But your black-and-white assertion that Inasa is either right or wrong in his philosophy is a bit asinine. Because the issue Ageless Bum and I are having is with how he acts on that philosophy. And yes, it is bias because he's basing Shouto's behavior strictly on his experience with Endeavor to the point where he claimed that he instantly knew he was Endeavor's son based on that moment. Not to mention saying quotes such as "WOULDN'T PUT ANYTHING PAST… A KID OF ENDEAVOR's!" Even if he turned out correct about Shouto being just as much of a douche as his father, that does not mean his logic in how he interacts with Shouto is justifiable or astute in evaluating someone's entire character. He would probably judge Bakugou in the same manner, true. But he is explicitly antagonizing Shouto specifically for being Endeavor's son and remarking that they're the same due to similarities in appearances, first impressions, and blood relation, to the point of stating he will never recognize either of them as heroes. Shouto's lineage itself isn't the main reason rather than Inasa's philosophies of heroism, but it's still a blatant factor in how he perceives Shouto as an individual and criticizes him after their first meeting.
Inasa did not get in a vendetta with Shouto, he decided to take an equally prestigeous school and avoided any confrontation or confrontation with him until their quirks started messing each other and he knows Shouto has 2 quirks. So he has consistently prioritize the exams and has shown no interest in getting in some petty squabble.
We don't explicitly know why Inasa refused his admission into U.A. yet. But if it was solely because of Shouto going there, a guy who he couldn't even have the time and chance to reply to, that is EXTREMELY childish. Just because he had a backup that is pretty much second best doesn't excuse that his reasoning for turning down the chance to get into the most well-renowned school purely because he got a bad vibe out of someone was very trivial. Dodging him in the same vicinity is fine and understandable. You don't have to be friends or associate yourself with people you dislike, especially if you think they're jerks. Turning down an admission like that solely because of one person you barely got to know though? C'mon. But again, this is only assuming that he turned down the admission to U.A. solely due to Shouto since that's what the evidence points toward so far until we receive more elaboration.
He also did not risk a comrade's life. He would need to at the very least think his actions could lead to that. Him and Todoraki fired(considering their bad quirk chemestry he seemed to assume Todoraki would switch) at the same time towards the enemy and their quirk got bad chemestry and end up doing things neither plan for at all.
Whether he intended to risk his classmate's life or not is irrelevant. What matters is that the reasoning and actions leading up to that are flawed and reckless to the point that he deserves blame for it. Both him and Shouto noticed beforehand that their powers countered each other's and that they both wanted the spotlight in taking down Gang Orca. Yet neither of them backed down or tried to change their methods to accommodate the situation and selfishly expected the other person to back down. Shouto himself didn't even try to switch to ice and got shot by a Gang Orca minion by being distracted by the argument. Knowing all of that with how their powers could be misdirected and that they had to delay the villains from rescuing simulated injured civilians, yet charging through with their attacks in the same fashion regardless out of pride. That is irresponsible. That is reckless. That is arrogant. And those are qualities of being childish.
If he end up continuing enticing Shouto you will have a point but considering his hot-blood temparement got him on a mess before and he has been avoiding any confontration from the start and just do his job, I think calling his behavior childish a grand exaggeration.
Avoiding him up until now is irrelevant now that they're in a situation where they have higher priorities at stake for both others and themselves, yet let trivial means of integrity evaluation and outside events distract and provoke each other without proper temperament. If two firefighters show up to stop a fire, but end up getting in an argument over who gets to use the hose due to some random insignificant event before then to the point that they either accidentally let a person burn up or suffocate for too long or end up shooting the hose at a nearby civilian, would you not categorize that as being childish? Age in any point on the spectrum physically does not mean you can't have your mindset be similar to that of an impetuous child. It doesn't matter if Inasa and Shouto continue this behavior because it's already gotten them to completely screw up who they should be attacking/helping and probably might get them to fail the license exam for all we know. You can't just give them a slap in the wrist for a one time incident that was bound to happen from how they were interacting when Gang Orca showed up, they need someone like Deku to beat sense into them. Inasa keeping composure up until this point doesn't matter for jack when he couldn't be the bigger man in a situation where it really mattered once he got triggered and wanted to show off.
Also not sure what "on the prowl" means.
"On the prowl" is a term referring to when a being wanders around to watch or search for something. It's typically associated with how predators look around an environment for prey. This is similar to how the Gang Orca and his minions appeared in order to look for heroes and rescuees to harm in the simulation.
In this and honestly most of the conversation we really agree. We just disagree on some of the definitions and outcomes. The childish part to me isn't that he wants to hold heroes to a high standard. The childishness is how he is going about his interaction with Todoroki. His anger/pride is blinding him to other possibilities and causing him to lash out somewhat.
This is what I'm pretty much saying. The belief is justifiable, but how he executes that when it comes to interacting with Shouto and acknowledging the priorities of the exam's situation is quite petty and pridefully unstable.