It's a good question, and the full answer is pretty complicated. You do produce antibodies to self-antigens. Without going into ridiculous detail (as I have been known to do *g*), there are a couple of rounds of elimination that the cells that comprise the antigen-recognition army are supposed to go through. In one round, cells that don't find antigens well enough get weeded out, and in another cells that recognise self-antigens are weeded out. Theoretically, this all happens before they get into the general circulation, so your body doesn't attack itself. Again, this is a vast oversimplification--you can look it up if you really want to understand the details on the molecular level. Or you may get to it if you keep on taking biology. ;)
This system doesn't always work, obviously--that is why people have autoimmune disorders, which are not very well understood overall.
Edit: It's not that your body reacts against the antibody as such. It's reacting to an antigen--something it recognizes as foreign. A part of an antibody may be recognized as foreign and attacked. As your professor has explained, the less 'foreign' the substance, the less likely it will be attacked. It's not exactly an all-or-nothing phenomenon, and you can also get sensitized to things you formerly tolerated if your immune system decides they're enemies.
Seriously, the simple answer to this is that the body has ways of recognizing what it considers 'self' and 'nonself' and acts accordingly, though not always perfectly. The non-simple answer is something I don't really have room to go into here, and may be beyond the scope of your biology book. Can I recommend a text? Parham's "The Immune System" is a really good one, not too long, and it has really good chapters on how these things go from genetic mutations all the way to functional cells. I think it's great that you want to understand this, but it's a topic that took a month to cover in med school. ;)