If you didn't watch the episode, I imagine you'd have a good reason to ask why he didn't shoot Tuco. If you did watch the episode, you'd know:
1. everything Mike explained to Nacho. If Tuco goes down, that means Salamancas. That means Nacho gets the screws put to him. That means he squeals and gives up Mike and then Mike dies a horrible death.
2. It's hinted at and isn't as explicit, but we learned this episode that Mike is a Vietnam Vet and was probably a sniper. "Why didn't you pull that trigger?" If you know any vets, you can imagine why he didn't answer.