Maybe Rockman World 2 (Megaman II GB) was rushed, but I think it's more likely the result of inexperience. The five GameBoy Megaman games were not actually developed by Capcom. 1, 3, 4 and 5 were developed by Minakuchi Engineering. For whatever reason, they were not contracted to do Rockman World 2, which fell to Biox instead.
Biox has never worked on a Rockman game before, or even games like it. Their prior work had largely involved puzzle games, and their talents were more evident on the GameGear. I feel most of Rockman World 2's problems stem from inexperience. The reason the other World games are better is because the Minakuchi Engineering handled each of them and gained experience with each game, making 3 better than 1, 4 better than 3, and arguably 5 better than 4 (although I'll have a soft spot for Megaman IV GB as that was my very first Megaman game I owned).