Well, try to see it from their perspective and empathize with their situation. Pot can indeed cause anxiety problems for many people, not everyone of course, but enough people that it's a known thing. I have seen it happen to several people, myself, and it happened to me, as well, and I had to quit.

Because of this, if they are to be responsible doctors, they have to rule it out. Even if a doctor believes that you are being completely honest and sincere, they can't know for sure that you know for sure whether or not the pot is contributing to anxiety. Some patients have strong self-awareness, and some patients don't. There is no way for a doctor to know which category you fall into.

So maybe consider some sort of compromise, such as being willing to take a break from pot and try medication, to see what happens, to put a doctor at ease. Then you can try to re-introduce pot, again to see what happens, to confirm whether or not it causes anxiety. Doing this under a doctor's supervision shows a willingness to empathize with their perspective and work together, but it doesn't mean that you have to give up pot for good, only that you are willing to do some experimenting.