Why do theists think it is a choice between intelligent intervention and random chance?

Random chance is a roulette wheel. Using both your theories you actually go against evolution. Nature doesn't explain how the universe started. You don't explain how natural systems can change others if you can't explain how there are more than one. Humans did invent certain gods but this doesn't say there isn't an ultimate God. In nature everything happens at some point and it is only about when, not if. That's as random as nature becomes.