Sounds like an uncomfortable situation... but don't give up! **hugs**
I went through a similar experience - I was working on my master's in vocal performance at the time. I was in school for something I knew I loved and knew I could do well, but the entire school (staff, faculty, and esp the students) intimidated me so badly that I sounded horrible when I tried to sing. Eventually, I left the school - it was just a toxic environment for me.
Was I a failure? Not at all, and neither are you, so don't you dare even think that about yourself! What it did was to make me reexamine what I wanted and who I was. Soul-searching ain't ever easy, but sometimes when we feel like we're hitting our heads against a brick wall, it's necessary.
Some things I would ask myself if I were you: what is it you love about nursing, or the idea of it? What part of school do you enjoy the most? The least? What is your motivation for going into nursing?
Not being in your exact situation, I don't want to give you specific advice since I don't know all the details. However, if you feel intimidated and uncomfortable where you're at, I don't think it's a good idea to stay. Nor is it a good idea to give too much credit to one person's opinion (including mine!). Are there other community colleges in your area? I know that where I am there are about 3 programs within a 20-30 minute radius of where I live, but that may not be the case where you are. Having a supportive environment can make all the difference! Also, you didn't mention if you had spoken with the professor privately about your anxiety - sometimes they may seem like Attila the Hun, but if you brought your concerns to him/her, they might be able to ease some of that frustration/anxiety and help you feel more comfortable. Professors are, after all, human beings themselves, and if you're uncomfortable, they may be too, especially if they feel like they're failing you as an instructor. Talking honestly and candidly with them may be just the thing. Or, they may still be a jerk, but at least you tried... and you know not to bother yourself trying to please the unpleasable.
Also, Tanzanite made an excellent point - is there anything else medical besides nursing you might have a passion in?
Don't give up! A lifelong "heart tug" is not something to be taken lightly or ignored. Your path may just be different than other students, that's all. I would still check out LPN/CNA programs, too - I know someone on another forum mentioned that an RN's duties are quite different than a CNA's, but it will at least let you flex your nursing muscles and perhaps lessen your anxiety a bit.
Hang in there, and don't be so hard on yourself, either. In my experience, nursing tends to attract the "tenderhearts" like myself (yes, I know there are scary people, but humor me here...) who also tend to be extremely hard on ourselves as well. You are obviously a very dedicated, hard-working, determined, and sensitive person, and that is exactly the kind of person a nurse should be. There are lots of options and lots of different routes, so check out all your options - especially programs at other schools where the faculty are more compassionate.