In an interview, art director Yasushi Yamaguchi was asked about how his team came up with the idea of having 2-players, he commented:

"The development of Sonic 2 was informed by two factors: the things we couldn’t do in the first game, and the response/feedback from players. The idea of controlling Tails came from programmer Yuji Naka, who wanted a kind of “1.5 player” game—something where it would be ok if the second player died. He wanted to allow for a tandem experience where both skilled and unskilled players could enjoy the game together."
Contributed by ProtoSnake