The rules (posted above) are that up to one manual chair must be stowed in the closet, provided the chair fits and the passenger pre-boards. There's no "booking", no "reserving". A manual wheelchair takes precedence over all other luggage, including flight attendant and first class passenger bags.
I'm sorry that you had a bad experience, and I'm sorry that disabled people are forced to compete with each other for scarce rationed resources like closet space, accessible bathroom stalls, accessible parking, and properly equipped rental cars. The sooner society recognizes that disability is not an exceptional outlier condition but part of the human spectrum, the sooner we won't have to trample each other in our race to get the closet space.
I don't believe that I act like an "entitled jerk". I do want my wheelchair, my means of mobility, to be treated respectfully and not thrown around like it's not important. I also don't want to be treated like I'm asking for special treatment when I merely want to travel like everyone else.