If you had to pick one, would you choose your pet whom you have raised and grown to love or a potential spouse who you like but he/she doesn't like pets and doesn't want one and asks you to find a new home for the pet? Also, he/she doesn't have a valid reason (such as being very allergic) other than pets are a nuisance, unnecessarily responsibility, dirty/unclean, fur everywhere, hates cats, etc.
For me, I would definitely choose the pet. I read a post elsewhere where someone put all sorts of restrictions on the woman's cat, and also declared no more cats after the current one. I found this to be extreme. No quite the same level, but this is similar to disagreement on whether to have children.