There are a lot of websites that I'm sure you could have your boyfriend read over but here are some general ideas of things for you guys to look into.
Other than being exposed to more illnesses and ways to get injured themselves, outdoor cats are actually very very destructive to local wildlife. I'm pretty sure they are like the #2 killer of wild native birds. Of course they'll also do damage to animals like squirrels, chipmunks, rabbits, and really any other type of small animal they can catch. Cats are a non native introduced species, so even though it's natural for cats to want to hunt, they are not natural predators of our natural wildlife. You can look up more about this but outdoor and feral cats are actually very very damaging to wild bird populations.
I've also had an outdoor cat attack me and my dog. Yup...a cat attacked us (my dog was on a leash btw). I know it sounds kind of funny but both my dog and I had to be treated - me because the cat bit my leg and it got infected, and my dog because the cat scratched his eye. His vet said that if the cat had got him a few millimeters over he very well may have lost his eye.
I never understood why it's okay for cats to wonder free doing whatever they please but if it was a dog or another animal instead of a cat then it's a big deal.
My sister just had to spend over $2,000 (so far) to have her indoor/outdoor cat treated for a broken leg. She could have saved herself a lot of money and the cat a lot of pain if she had just kept him inside. Her other outdoor cat just plain out disappeared. No one knows where he is or what happened to him. Needless to say she's decided that she'll be keeping her cats indoors only from now on.
Sorry for such a long post! This is really a pet peeve of mine, if you can't tell. Cats can live perfectly happy lives staying indoors, or if people do what you do and take them out on harnesses. If you live with your boyfriend, than getting a new pet should be both of your decision and not just up to him. Even if it's not your cat, you'll still have to deal with it. If it where me, I'd tell my boyfriend that either he agrees to keep the new cat indoors or else I wouldn't agree to getting another cat.