The Amiga always supported 2-button controllers, compatible with Sega Master System and Mega Drive/Genesis pads. The mouse has two buttons, which act as Fire 1 and Fire 2 if plugged in as a joystick.
But for some idiotic reason, 90% of Amiga programmers back in the 80s and 90s never even considered that someone out there might want to use a controller with more than one button. We didn't even get keyboard controls as an option in most games.
Since around 1992 Amigas have supported control pads with seven buttons (the CD32 pad) which barely got the support it deserved either.