That depends on whether or not it's something you truly love. Saying it can't be done is implying no one has done it--and that most definitely is far from the truth.
It depends on what animals you're breeding (obviously, you won't get rich breeding cockapoos--but what about race horses, high end herp morphs, or massive numbers of feeder rodents or insects?).
Folks have gotten 'rich' breeding all of these things. It depends on how much capital you start with, how smart your business plan is, the quality of your stock and how well it holds its value, and more than a bit of luck.

You won't be looking at becoming a billionaire, but 3 figure annual incomes are within your reach. Just be prepared for the massive amount of work and space it will require.