is it ever appropriate to downvote for that reason [the way that the OP handled a situation irritated/frustrated me]?
Never. You don't vote just because OP handled the situation badly. In fact, many of the post in TWP branch from situations where OP didn't handle the situation in an appropriate way.
But that's no reason to DV. You DV if the post lacks research effort, is not useful, is rude or abusive (case where you should also flag), etc.. Never because OP handled the situation wrong and you felt irritated by that.
We are here precisely for that reason, to guide and correct people in a professional environment, helping them grow and learn from their mistakes or faults.
What you did, that is, refrain from DV and post a helpful answer so OP can learn and grow, is the way to go.
Edit: I'd even go a bit further and say that DV-ing for such reasons is getting very close to revenge down-voting, or systematic down-voting, something very discouraged here and in the whole SE network.
Don't let emotions get in the way. If a post/comment irritated you or frustrated you, take a short break from TWP, and come back to the post (if you want) when the frustration has subsided. It's part of keeping a Professional attitude, something paramount for this community.
Anyways, knowing the reason why some folks DV is something we can't guess, and getting explanation on the reason for the DV seldom happens (some folks just DV and move on, although it would be way better if they provided feedback for improvement).
For a related reading, check this old MSE thread: Encouraging people to explain downvotes
Also this one: Why isn't providing feedback mandatory on downvotes, and why are ideas suggesting such negatively received?
(I can't find one which had an answer by Shog9 or Jeff I think, that illustrated the concept in a more joke-like manner... but nevertheless to the point).