Nagato was a kid back then so a lot of things could happen that would make him mentally unstable. Look at Garra for example. He was ignored by everyone becasue they all viewed him as a monster. Then they tried to kill him, which drove him to set his own goal of killing people in order for "his existence to have meaning".
Im not saying Gaara was in the right before Naruto changed his ways, Nagato however was hyped to have had the worst possible things imaginable happen to him which turned him into a psycho with a disturbing ideology for a security blanket.
So far, at least for me his reasons are not all reasonable ( reasons for killing people are never really reasonable but still ) if you weight it against what he has doen and how many he has killed.