Unless you're both really committed to having any sort of pet then it would be a disaster to get a one. And you certainly don't get a dog with the idea that it would hopefully cure your fear of them.
Dogs are hard work and they need commitment for their lifetime, which can be as much as 16 years or longer.
Commitment means training, regular exercise, companionship for the dog, care and nursing when they get ill and caring for them when they get old. Paying for vet treatments, insurance; dogs aren't cheap.
Commitment also means you have to plan everything ahead. So no deciding on Friday afternoon that you'll go away for a romantic weekend together, not unless you have someone to leave the dog with. Days out have to be organised allowing for the fact that a dog really shouldn't be left alone longer than about 4/5 hours.
You say when you have children walking a dog wouldn't be your priority so I'm guessing all the the above wouldn't be things you'd want to prioritise either.
You are being the sensible one here. You know what you can and can't do and how you want to live your life.
He isn't being realistic in expecting you to go along with his idea of what having a dog involves..
He's right, having a dog can be a great addition to the home, but only if everybody in the home wants one.
You need to get this ironed out before you move in together.
How do you get round it? You don't get a dog.