I don't own harry potter just this theory

Ok so I've been wondering how do muggleborn witches/wizards have magic?  I'm pretty sure it was explained in the books but it's been a while since I've read them and forgot what said reason was so here is what I think:

Muggleborn witches/wizards are the reincarnations of half or pure blood witches/wizards.  Since they are the reincarnation of pure bloods or half bloods they get magical abilities from their past life.