Last semester, I took class A and loved the material. It was a subject I excelled in and professor A' was someone I understood well.
I thought it was perfect to take the course 2A and make A' my thesis advisor, but this entire semester, he missed many classes (due to sickness and/or being the Chair of our department), was only available for 'pop in' office visits, rather than scheduled ones or scheduled office hours, and we rarely had homework we could do, because our class was riddled with confusing theory and no examples.
For a grade, he asked us to learn and present material in class. I'm a student who needs to bounce ideas off others in order to really understand material really well.
Since no one (fellow grad student wise) could help and he was always unavailable, I stuck to books and mathstackexchange.
I got turned around many times, and when I had to present, he constantly interrupted me to tell me "what [I] meant to say". After 40 minutes, I got so worked up I started to tear up.
I felt like the time I spent trying to work through material by myself was worthless, and anything else I could say wouldn't be "up to snuff" in his eyes, but I pressed on through hiccups and tears. I know he was trying to make me a better student, but I'm not sure I can take a year of trying to do something right on my own, rarely meeting up with my thesis advisor, and falling flat during my thesis defense.
Questions: do I find another thesis advisor? Is this just a personal problem, and I should consider counselling?
You've not really commented on your thesis advisor's role as a research supervisor, which is quite different from being an instructor. Someone can excel in one role but be [almost] incompetent in the other.
Consequently, it's hard to give you solid advice. The basic question is if your advisor's unavailability is impeding your research progress. If so, then you should definitely explore other options, if possible. For instance, look for a co-advisor for your project with A'. If no options with A' pan out, then you should consider switching advisors.
However, if the teaching style doesn't carry over into research issues, then it may be worth your while to wait and see if things improve.