For me, the answer is: the human immune system is weird and error prone.

Perhaps you got better because your innate immune system cleared Covid--you may not have antibodies. Perhaps your immune system keyed off something screwball on the virus--you may have antibodies that are less effective for other variants. I can go on.

Getting the vaccine means that I know I have antibodies to the spike protein in particular--which seems to be common to all the variants.