I once moved into a shared house that had a dog because my flatmate decided to buy one without consulting anyone immediately after the lease was signed. I didn't agree or consent to this, but was stuck in that situation for a year because I couldn't afford to break the lease.

They then expected me to take on a share of the responsibilities of caring for it (which I did despite not being a dog person, because I didn't want it to suffer or be neglected) while having none of the ownership. If I tried to stop it from stealing food or damaging furniture, it was "their dog" and how dare I interfere. But when it came to walking and picking up after it, suddenly it was "our dog" and how dare I neglect my responsibility.

All this to say, there's a huge difference between consenting to "living with someone else's dog and occasionally helping out" and "becoming co-owner of said dog who is just as responsible for it". OP has had to fight for a long time not to have to share a bed with this dog, so they're clearly not in the second category.