So, Alex doesn't really hate heroes, what he hates is the term "hero", because he was called that even when he made so many mistakes. So he doesn't feel like one and his hate of this part of himself is what makes him get annoyed at this world. At least, this is what i think.
It is kind of annoying that MC don't really get anything in worlds aside from points to buy things... Heck, MC has the biggest treasury of humankind and yet he is *****ing he does not have enough information about magecraft nor enough points to buy the next part about it? Considering what is possible to do with information I wouldn't doubt if it can be considered a treasure and be in the Gate (after all if you can find even chocolate there why wouldn't you find about magecraft?)