I don't see Stallman's statement as to whether his birth had a good impact on the world or not as necessarily arrogant. Arguably, that's a question everybody needs to or ends up asking themselves: on balance, has my existence been a positive one?

While there might've been an open software advocate without Stallman, it can't be seriously said that the world would've been better off without Stallman's advocacy. And thus, on balance, the world's better off with Stallman than without.