High notes and breath control in classical singing?!

High notes and breath control in classical singing?

I am a young bass who has been singing on my own and in some choirs over the past few years. My voice has gotten too big for the choir and I'm starting to think about classical/operatic training. I'm starting my freshman year at college and have been studying this summer with a local voice instructor. My voice is big, and rich, and the best thing about it is that I think I have a lot of potential and there is a lot of room to grow. Two of my trouble areas are pretty normal---getting more strength in my top register and having better breath control. So here's the problem. My voice teacher has told me since we began that both those are a result of proper technique. I understand that and am working on it. But she makes it seem as if she could pull anyone off the street and make them sing high C's for thirty seconds right then and there with proper technique. I've heard that that is the beginning but it takes time to actually develop and strengthen them.

Am I wrong?

no, you are not wrong. these two areas take a lot of time to develop and master. the first few steps in training often bring big splashy results ( high C's in 30 seconds), but we're after the long term, long lasting, solid results.
A metaphor I'm fond of: we can all run. some of us are just glad to catch the bus in the morning, some people jog daily, and some are really trained, like the marathon runners. Amongst the trained runners, there are specialists: sprinters, 100 yds, 1 km, 10 km, etc. learning these specialties takes time and practice. Sure, showing someone how to catch the bus is easy, but teaching someone how to train for a marathon needs know-how, and the ability to do it yourself.
If your teacher has the ability to "go the distance" herself, then she probably knows what she's talking about. If it seems like it's just hot air or showing off to impress you, either ignore it and get on with your own task ( teachers are also only human, after all), let her know that this bothers you( and prepare to change teachers in a big hurry, because teachers are also only human after all) or let it serve as a further chapter in the on-going lessons of human development.
Best wishes to you, and keep on singing