Yes, proofs by contradiction appeal to new mathematics students because one can just wander around until a contradiction pops up and then you're done! Of course

Yes, proofs by contradiction appeal to new mathematics students because one can just wander around until a contradiction pops up and then you're done! Of course, these meandering proofs are harder to understand, and it's easier to make mistakes when there are lots of unnecessary derivations along the way. I've always found proofs in algebra and topology to be less intuitive and consequently often had to resort to trying to find a proof by contradiction and then unraveling it for its essential elements to make a better, clearer proof. Proofs in combinatorics (often by contradiction) don't even seem to have an better, clear proof buried inside; they are just essentially inscrutable.