Because you are not being obliged to choose either option. 'If I were to run, I would win the race', doesn't mean that you have to run in the race. 'If I were to eat snails, I would be sick'. You are not obliged to eat the snails. 'If I were to choose' - you are not being obliged to choose anything. You might decide that you don't want to choose. 'If I were to' means that you can avoid the whole situation if you want. You still have two options - choosing or not choosing, in the same way that you can choose to run or not run, or to eat snails or not eat snails.
I can see how you are confused though with choose. Can we change it to another example to make it clearer?
If I were to choose to die, I could either be hung or drowned. But actually, I'm not going to choose to die, I choose to live, so I don't have to pick either death option.