Yes, that core belief that women should receive equal opportunities and fair treatment, and that our sex shouldn't be used to discriminate.
I believe that, but I am not a feminist.
You know, I spent years and years saying the same thing. I spent a long time insisting I wasn't a feminist, because people like you were so incredibly derisive of feminism as a whole, and constantly held up the very, very worst possible examples of behavior, and treated them as if they were representative of the whole. People like you created a narrative centered around "feminazis" and "man-haters" and crazy women. Enough so that I didn't want to be associated with that label, despite the fact that my actual beliefs and feelings and actions were clearly in line with the core of feminism.
It's only now that I've aged, and I no longer give a crap what people like you say, that I have embraced feminism for what it actually is instead of the caricature that was painted.