I'll be more specific. In a determined world there is no choosing.
Choosing is a deterministic operation that inputs two or more options, applies some criteria of comparative evaluation, and outputs a single choice, usually in the form of an "I will X", where X is that which we have decided we will do.
And you're saying this never happens? Come with me to the restaurant. Watch the people walk in, sit at a table, browse the menu, and place their orders. How was the literal menu of options reduced to a single choice, if not by choosing?
If we stick around, we will notice the waiter bringing each person their bill, holding them responsible for their deliberate act.
Like all events, these events were causally necessary from any prior point in the past. Causal necessity does eliminate choosing, it assures it will inevitably happen.
One's own impression of what one is doing, or of what others are doing, is subjective.
Watching people in the restaurant reducing a menu of options into a single "I will have the chef salad, please", is an objective observation, not a subjective impression. That's why I use it. Everyone has seen people actually making choices in the real world.
And we just objectively observed choosing actually happening. Cool, huh?
Subjective isn't up to the task.
So, are you suggesting that we, as objective observers, were just imagining that people in the restaurant were making choices? We cannot see inside their heads. But we did see a menu of options going into it, and a single choice coming out of it. Choosing happens. It is a real deterministic event that occurs in the real world.