Presenting is a skill. If you do not have it, you do not meet the graduating requirements and you shouldn't be able to graduate.

They have an obligation, maybe self-imposed obligations, up to some point, to support you in developing your skills when you are having additional difficulties. Letting you pass courses at a lower academic standard than your peers; you cannot expect such an arrangement.

You will have to put in much more effort than your peers to meet the same academic requirements.

You were given a fair chance to show up and present, were you not? It is up to you to take that chance.

Now I understand mental health can be very debilitating, up to the point that you cannot function properly, either academically or professionally. And it seems you are trying to solve your problems alone.
If you are having such difficulties, maybe this is not the right time for you to take on these challenges. Maybe instead of focussing on your studies, focus on becoming functional. Once you can do that, take on academic challenges like presenting. Presenting shouldn't be about overcoming anxiety in the first place.

If you never get help, it may will never get better. From their point of view, why should they go to extreme length to accomodate someone with anxiety disorder when that person takes no action to overcome the challenge herself/himself?

When they have to make an exception for you, on medical grounds, it is perfectly reasonable for them to request a doctor's reference, or something similar.

This may sound like a harsh reply, and maybe one you wouldn't have gotten on the anxiety forum. but these are my honest feelings.