Not knowing your situation, or who is in charge of the finances, maybe he feels you can't afford it? Is it so hard to respect that? The economy is not exactly robust right now. In my family, we discuss all expenses, and there's no nagging or attempting to convince someone to spend on something if the other isn't comfortable for some reason.

If you guys keep separate funds, do what you want with your money. If you keep joint funds, add something to your self care mix that doesn't cost $200.

exercise is not a luxury; it's crucial to my mental health.
I don't buy this as an excuse to spend another $200 a month for a exercise class . I have an ongoing depressive disorder that is greatly improved and managed through regular exercise and self care, plus regular medication. That doesn't mean I spend what my husband feels is inappropriate amounts of money to manage it.
There are lots of ways to exercise, get that mental refreshment, that don't cost money. Or, perhaps DH might support spending the money to get better treatment to manage your depression, if what you are doing now isn't working for you.