I was browsing on this forum reading about a completely different topic, but had to register an account just to reply to you, because I am in EXACTLY the same position.
My wife and I did take a "Discover Scuba" course, which started with the same feeling of panic anytime I'd put my face in the water. However, the instructor actually helped me successfully breathe through the regulator and enjoy swimming around the pool. It took concentration to stay relaxed, but I did it.
Fast forward about a year or more, and we decide to get certified.
One of the first tasks in the pool was to use the regulator underwater without a mask, and without pinching the nose. I could not do it. No matter what I do, I always breathe a little bit though my nose, and this causes sheer terror as I feel like I will inhale water at any second.
I then learned that breathing without a mask and an open nose will be part of the certification process. I instantly knew I wouldn't be able to get past that, but I continued with the lessons.
At another point, while learning to be neutrally buoyant, I had a few drops of water get past my regulator and I panicked. I hit the inflator and popped to the surface immediately. Then it happened again, and I was just done. Over it.
I *can* scuba. But it takes so much concentration that I cannot relax. And I know that I will panic at the tasks that are required, like flooding or removing the mask, etc. That leads to intense dread about actually being 30 or 40 feet down and experiencing this level of anxiety. I have given up, and I'm totally ok with my decision. This is supposed to be an enjoyable activity, not something that causes fear of death. I have a claustrophobic reaction to it, and I'm not interested enough to work through it. I gave it my best.
For as long as I can remember, even snorkeling was difficult for me. The thought of inhaling water - any water at all - caused uncontrolled anxiety. I could only snorkel by holding my breath and breathing only when necessary. Smooth breathing was out of the question. I even have an issue with the typical method of "crawl" swimming, where you take a breath from under your arm. Too close to the water's surface. Been this way since I was a child, and I still don't swim that way to this day.
My biggest disappointment is that my wife really wanted us to try this. But being that it's something we will never share, she quit the class as well. I encouraged her to continue, but we both wanted this to be a "we" thing, which it was never going to be.
The dive shop I patronized was super-understanding about my issue, and refunded the entire price of our course, minus the cost of the one class we did take. This includes the cost of the Mexico trip that they organize for certification. I'm guessing it's not uncommon that people "tap out", and they have an incredibly fair refund policy, which was nice. But honestly, even if it was 100%n non-refundable, I'd still have quit.
Don't feel bad about giving up if that's what you have to do. No, it's not for everyone. It's not easy for everyone. For me, I deem it's impossible. I can't see any way I'd get over the fear of being 40 feet down and having a panic moment that can cause me true injury. It's not worth it to me.
If there's any positive to the experience, I HAVE learned to snorkel. Being near the surface, I've been able to get over the anxiety of inhaling water and I'm able to enjoy that activity. To me, that's a win.