We can backup a few more steps.
The source of “believing” in choice, or that you can choose any course-of-action, is Control. People believe they are in-control of “themselves”. Arguments can be made for-or-against. And those arguments also apply to any other organism, or possibly, all existence and non-living matter. So, why do (some) people believe they are “in-control of themselves”? Is this not moral agency? Is this not self-identity, your self-consciousness?
If you don’t know when you are, or are not, in-control of yourself, then “choice” is a moot-point. As the Determinist would say, Choice is an “illusion”. (but compared to what?) A Hard-Determinist must say that moral agency, self-control, is not even possible. There is no means by-which a person could ever be “in-control” of his/her own actions. Because: Control of what by Whom?
I’ll go all the way back here… what is “Self-Identity”, except, as defined by the set of choices (or actions) that any person or individual has taken throughout life?
You can call all actions “Choices” insofar as a person is also “willing to take responsibility for them”. This is the sophistication and complex part. Animals don’t need to “take responsibility” for themselves. Animals live in Nature. And if an animal fucks-up, makes a mistake, makes a “wrong choice”, then it is usually injured or killed (by a predator). So, in-Nature, Choice is do-or-die, and the very factor of “survival of the fittest” and “evolution”. Evolution is only “right choices”, leading to survival and increased reproduction.
In Humanity, “Choice” is abstracted to a higher level, and doesn’t necessarily represent immediate-survival, but rather projected-survival. In other words, let’s say you could make superior choices for the next 20 years of your life. So you choose the “right choices, course-of-action”, and such choices lead to a superior state or elevation of life, by your own definition.
Humans have the ability to project “Choices” far into the future. If you do this, then that happens. If that happens, then you do this. Etc etc etc. Choices are means of “selecting” a future.
A Projection of the Will.