I think it depends what type of pet it is. I mean, a chinchilla (or several) or caged pets can all be kept in one room with the door shut if one person doesn't want the pet. On the other hand, if one person wants a dog/cat and the other doesn't... well the other's gonna have to actually live with the pet so I think that's different.
I think the best way is to reach some sort of compromise. Maybe that's not possible in every situation, but in some I think it is. A good example - Now, I live by myself and pay for everything, but at one point, I was living in an apartment where my parents were paying my rent (I was paying bills and everything else, but my $8/hr job for 15 hours a week wasn't paying for my rent)... my parents were saying no more pets but I wanted to get my dog... and we came to the agreement that I could get my dog if I somehow lessened the "pet load." I ended up re-homing my rabbit, my degus, and some long-standing rescues (chins) that I had just been slacking on working to find homes for... and everything was fine. With the amount of animals I had, I actually agreed that it was better to find these guys homes anyway, cause I was slacking on giving them all individual attention. But point being, like if the number of animals maybe is getting too much, maybe some agreement can be made to work things out. I suppose this isn't a good argument if you have 24 chins and wanna make it 25, but I suppose it works fine if you want to get a dog or cat and could live without your fishtank or small animal(s) because you'd rather have the dog/cat.
If he thinks that cats/dogs are messy (I just read the above posts, sorry), then maybe try adopting a grown dog/cat that is already housetrained and everything. I wouldn't suggest getting a puppy as that's only going to reaffirm his conviction that they're messy. But if you get one that's already housetrained and knows how to let you know that they have to go, then they're pretty clean (minus the shedding of course). I even like the idea above, about fostering. That way, you don't have the animal forever, and I was just looking to foster, and one of the places I looked at said that if for some reason you couldn't foster any longer and they had to take the dog back, that was fine... I don't know if a lot of places are like that, but I think that's a good way to "try out" a dog or a cat...