It's not entirely clear, but in Sonic CD for the Sega CD, Amy was captured my Metal Sonic and Sonic had to save her.
Number one:He saves her. Number two:He protects her.Number three:She thinks he's hot.Number four:He is a hero.Number five:He is her first friend.
Sonic loves her
Sonic is 15 and Amy is 12. I used the Sonic Heroes manual as a reference.
Sonic saved Amy's life so that's why she developed a crush on him.