My [29F] boyfriend [33M] told me he hates my dog and gave me an ultimatum

I bought Sadie when I was 15 years old for $2- some little kids were on a bridge near my house acting weird with a paper bag, and when I went up to them I saw that they had a tiny puppy, too small to be away from her mom, that they were clearly intending to throw off the bridge. I gave them the $2 I had on me and took her home and my parents let me keep her, and we've been BFF for almost 15 years.
My boyfriend, Alex, and I have been dating for 3 years. He's generally a really great, funny, warm, solid guy, but every fight we've ever had has basically been about Sadie. He'd never had a dog or lived with a dog before, so when we started dating he was often annoyed at my lack of spontaneity because I had to schedule around walking my dog, or make arrangements for someone else to walk her. Once he finally caught on that walking my dog was something that wasn't optional, Sadie started hitting that point in old age where she got a little gross.
Everyone who has had a senior dog knows that there's a point where, even with the best vet care and otherwise perfect health, they get a little smelly and a little gross and become a 'face only a mother could love' type dog. He started getting more and more frustrated that I was putting time aside to care for my dog; nothing insane, just taking her outside more because she couldn't wait as long between walks, having to clean my house more to get out 'dog smell,' having to get her groomed more, more regular vet appointments. He and I still spend a ton of time together, but he started to get mad that he had to mostly sleep at my house (I live alone and he has roommates, I live closer to his work, my house is overall 'nicer,' so I think this is just a fairness thing vs. a serious problem).
The other day, though, he gave me an ultimatum. He said that I need to see if my parents will take Sadie or otherwise 'get rid of her,' because he's tired of 'our' lives revolving around her. He said that he thinks she's gross, he doesn't want to pet her because she makes his hands smell, and he's tired of always having to go to my house instead of his. He also suggested, weirdly, that he'd move into my apartment with me (in this neighborhood he doesn't want to be in?) if Sadie was gone.
For me, this is a no brainer. I bottle fed this dog as a puppy, and to abandon her as an old lady would be cruel. I admit, she's pretty gross, but she's MY gross baby. Plus, the life span for the breeds my vet thinks she is (beagle and pekingese if you can imagine it) is around 15, and she's... around 15. She isn't going to be around much longer, and at the first sign that her quality of life has deterioriated or that she's in pain, I will let her go because I wouldn't keep her alive just for me.
Am I being unfair to choose a dog over a person? I am truly in love with my boyfriend, and really saw a future with us, and I'm devastated that he hates such a big part of my life and feels that she's an impediment to our future, but I just can't get rid of her.
TL;DR: My boyfriend wants me to choose between him and my senior dog.


Source.