This might just be a general Japanese-Language question, but I noticed, that Iida calls Ochaco with the honorific "kun", instead of "chan", or "san" for example.
Why is that and what does it say about Iidas character?
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From what I was able to find out, -kun, while mostly used for males, can also be used for females. According to this,
Kun for females is a more respectful honorific than -chan, which implies childlike cuteness.
-san can also be used but according to the same source as above,
Due to -san being gender neutral and commonly used, it can be used to refer to people who are not close or whom one does not know. However, it may not be appropriate when using it on someone who is close or when it is clear that other honorifics should be used.
I think this just means that Iida tends to be formal, or even more formal, towards females/girls (since -kun is informal when used among fellow boys, but despite this, he still acts serious even with his male classmates) and might be just his way of showing respect.
I searched for the answer too but couldn't find anything. I am not sure, but according to my assumption and observation, Iida uses 'kun' because he's trying hard to speak in a more informal way instead of using sophisticated words as he doesn't want others to know that he is a rich guy and be called a "Rich boy". I mean, you see as Momo is also from a high social status family, she tends to use 'san' (which is formal), so maybe (in a comical way from the mangaka's point of view) Iida thinks that using 'kun' (which is informal) even for the girls will help him blend more to being a "less wealthy boy"?
I am saying this taking reference from season 1 episode 9 where Iida unintentionally uses formal/sophisticated speech at a cafeteria in front of Ochako and Midoriya, so Ochako asks him if he is a rich guy, then he reveals that he is in fact the younger brother of Ingenium and tells them how he was trying his best to change his way of speaking.
But after this long paragraph, I am still not sure. Maybe our fellow friends who read the manga may have a better explanation because am only an anime watcher.