Since I was just talking about this recently, here are two disparate examples of why I personally see no reason to identify as a Buddhist, even though I have certainly learned much from various Buddhist authors and thinkers (especially from the secular Western variety). Debating different ideas and perspectives is fine, of course; I’m simply not interested in squabbling over precisely what one has to accept or believe in order to qualify for the official label. It strikes me as a completely off-track and self-indulgent argument to have.
There are things that I credit Buddhist philosophy with teaching me that I’ve accepted as self-evident truths, but if it turned out that I was mistaken, that they did not, in fact, have any basis in anything ever taught by the Buddha, well, so be it. I would trust my own experience, judgment, and the truths themselves and leave my notions of “Buddhism” behind. Fixating on the persona behind the ideas that resonate with you is misguided. Labels aren’t important. Just this.