Why exactly is Saitama a hero? Saitama, who trained for three years only doing 100 push-ups, 100 squats, 100 sit ups, and ran 10 kilometers every day, became a "superhero for fun", but what does he mean by that.

Is he really only doing it "for fun" or did he have motives but then forgot? Because normally a hero does it for a reason like to protect the ones they love, to defeat all evil, to prove that their strong, to protect something like humankind, etc.. Or is he really just doing it "for fun" because he's bored. Or is there actually a deep meaning for those words?
Saitama's real reason to be hero was intended to be satire over common cliche reasons of most heroes.

If you think about it, it can be literally rephrased as "Does one really needs reason to help another people", which itself is actually nice idea for manga to show, if you are looking for some deep meaning.