Normally the emergence of a contradiction in the course of a proof serves as a red flag that something's wrong. When proving by contradiction, you're operating without the safety of these warning signs as you progress through the proof. If you reach a contradiction, you have to question whether or not you got there suspiciously easily.
If you're aiming for something more specific than just falsehood -- "not X", say, as in the contrapositive approach -- you might be less likely to get there incorrectly. If you reach a contradiction along the way, you don't go on to say "and I'm done since contradiction implies everything including not-P", (even though technically speaking this would be perfectly valid) instead you question where you went wrong in the proof, because this is too easy.
But yes this certainly feels like more of a fuzzy psychological argument doesn't it. I don't know how (or if) you could formalise a notion of "how susceptible is this proof tactic to accidents".