[ltjohnson]

Speaking as an almost not-amateur (finishing my PhD this year, and working on getting a faculty job), you're both right.

Logically, there's nothing wrong with proof by contradiction. As long the steps between "Assume P is true" and "therefore FALSE" are valid, you have a valid proof that "P is false".

The issue with proofs by contradiction is psychological, but it's important not to ignore such things when you are doing math. Proofs are written for people to read, and people make mistakes in reading, writing and constructing proofs. The longer and more complex a proof is, the more likely it is that there are mistakes. I can't speak for all fields, but in my field (statistics) proofs by contradiction are acceptable but not in style and constructive proofs are generally considered to be more informative.