Consider these two examples...
1: I never choose a starter in my local restaurant. I always have the "soup of the day"
2: I never get to choose a starter in my local restaurant. I always have the "soup of the day"
The context of #1 strongly implies that I could choose some other starter dish from the menu - I just don't want to exercise my right to make a choice.
But #2 strongly implies I don't have a choice. Feasibly the restaurant doesn't offer a choice of starter, but more likely it's because I only go to the restaurant with my wife, say, and she always insists on making that choice for me. Whatever the reason though, the strong implication is that I would like to be able to choose for myself, but I can't.
In general, to get to [do X] implies that doing (or having the opportunity to do) X is desirable. Which is usually the case with something like "choosing / having a choice" - but as my example above shows, there can be contexts where someone doesn't care whether or not they have a choice. In which case they wouldn't refer to the situation in terms of getting to choose.
In OP's cited context, including get to unambiguously conveys that the speaker would like to have a choice. He's effectively saying Why shouldn't I choose, rather than you? If it's not included, that implication could still be contextually relevant, but feasibly the speaker isn't thinking that he should have the choice.