But asexual means reproducing with yourself

Yes, asexual reproduction means reproducing without a partner. However, asexual reproduction and asexuality are two different things. Asexuality is a sexual orientation. As far as I know, asexual people aren’t capable of asexual reproduction any more than people with other sexual orientations.
Words can have multiple meanings. If you think that’s strange, I’d have to ask you which strange you’re referring to; strange as in unknown or strange as in odd. Then again, odd is the opposite of even. Don’t even get me started on that one.
Unlearn your “But in school I learned that it means this.” attitude and embrace the replenishment of your vocabulary.