At first glance, the Hero Killer looks like your standard anti-villain. His ideals are to flush out heroes who would use their status for their own desires and breed heroes who work purely for the sake of a better society. The narrative in fact agrees with these ideals, as the appearance of Deku and Todoroki force Iida to question his own desire for revenge, and it is mentioned that the crime rate actually decreases where the Hero Killer makes an appearance. Thus, it would be easy to assume here that the only reason our protagonists are fighting him is because the way he goes about it, killing heroes, is wrong.
However, there are deeper tensions within his ideals that reflect deeper tensions throughout Boku no Hero Academia. If we examine the Hero Killer’s target, Ingenium, more closely, we see that he isn’t a selfish person; he openly states that he’s glad his work helps many people. Granted, what we know of Ingenium is filtered through Iida’s admiration for him, but even so, it is unlikely that he was targeted for selfishness alone. In fact, Ingenium could easily be another shonen anime’s protagonist, relying on and being relied upon by his friends.
This, however, is the most likely reason he was attacked. As stated in Mother’s Basement’s Boku no Hero Academia – The Anti-Naruto, Boku no Hero Academia posits an individualistic view of strength through defeating others in competition, the opposite of the strength through friendship that shonen anime like Naruto represent. Thus, while the Hero Killer does believe that heroes must work altruistically, he also believes that they must be strong, highlighting the tensions between the value of strength and the value of compassion.
In Boku no Hero Academia, heroes are integrated into society as celebrities, and reaching that status is their primary motivation for becoming stronger than their peers. Mother’s Basement isn’t wrong to call this social structure capitalist; even All Might understands that he is using the stability of his position as the number one hero to stabilize society. His deteriorating health heralds the crumbling of the current societal order, and he is, in essence, too big to fail.
Of course, Boku no Hero Academia doesn’t really agree with the capitalist society that it presents. If that were the case, then Endeavor would be the number one hero instead, and Boku no Hero Academia, as it says at the beginning of every episode, is the story of how Deku became the number one hero. To quote Mother’s Basement again, “Deku’s ultimate purpose seems like it may be to remind the world of what the true role of a hero is: to help others,” and we can see that this includes helping his peers, not just from the way Deku stands between Iida and the Hero Killer, but also how Deku helps Todoroki overcome his trauma even at the cost of losing their fight.
And while that willingness to meddle in others’ business is part of the reason the Hero Killer respects Deku, it’s only after Deku shows what he’s capable of in combat that the Hero Killer says he’s worth letting live. His ideals are contradictory in complex ways that showcase the difficulties of reconciling Deku’s compassion for others with the competitive structure of the society he lives in, and understanding that helps us to appreciate that society in Boku no Hero Academia is more than just some abstract thing that villains want to destroy for simplistic reasons like in many other shonen anime. It is as complex and flawed as the characters who live in it, and that allows it to shape villains like the Eightfold Cleansers, who have real grievances towards society and real loyalties towards those who shelter them from it, as well as heroes who can understand them through their own trauma with growing up in that society.