Gotcha. To try to at least make compatibilism comprehensible:

If physicalism is true, then desires are some combination of physical states and/or processes.

Whether determinism is true or not, you are inevitably going to ‘choose’ those desires in exactly the libertarian free will sense, by definition. The only things you’re not free to choose are the things you don’t choose. You could have chosen differently - if a combination of processes in your mind had given a different result, which is to say, if you were a different person in the relevant sense (which could be quite minor in the case of an arbitrary choice, but major in the case of something that speaks to your core beliefs).

The only real difference between this and libertarian free will is the belief that desires aren’t fundamentally mysterious. It might founder on some other rock (if, for example, determinism is false, or if there’s some other property of free will not being captured here, or if there’s no such thing as ‘self’, or if you define brain processes as being outside of self), but hopefully it’s at least a bit more understandable how a person could believe that, and what exactly they believe.