First of all, critiquing can be valuable! In fact, not "can be," but is. I belong to a face-to-face critique group that's been meeting for at least 16 years, maybe longer; I'm not quite sure. And I've been critiqued in other situations: conferences, one-time manuscript exchanges, even in a second crit group (online) for a short time. Besides critiquing for my long-time partners, I do a whale of a lot of critiquing as an ICL instructor, I've served on critique faculties for conferences, and I even run a fairly frequent critique contest on this blog. But, sometimes, critiquing can be weird.
For one thing, it's so subjective. One person's "Ugh" is another person's "Couldn't put it down till 4am." A personal rule of thumb I've come up with is this: If TWO people say something is wrong at a certain spot, something is wrong at that spot. They may or may not agree on how to fix it, and you may or may not take either or both suggestions. But you have to find a way to answer the objection.
For another thing, it's the critiques that make you feel worst at the time you receive them that often turn out to be the most helpful. I've found that it's sometimes best to put the raw, torn-to-shreds thing to bed for three days or so while you kvetch, and then take it out and look at it. By then, I usually "know that I know that I know" which parts really do need to be overhauled, and which advice I'm going to decline and why. And specific ideas for solving the problems are usually beginning to form.
Then there's the irony that a critique group may not always help all that much. Sometimes, frankly, if all the members are newbies they are the blind leading the blind, and I know some agents advise their clients to get out of critique groups that are "holding them back." It's often best to join a group that has a mix of newer and more seasoned writers, and/or to be sure the people in the group are seriously working to improve craft, have studied and written long enough to have gained at least basic knowledge, read widely, and know something about the field in which you write.
Here's one more thing I find a tad strange: critiquing is the process of identifying what is and isn't working in a piece of writing, and there is "always" something that can be improved. Except ---certainly there are times when writing that is actually ready to be marketed is submitted for critique. We, as critiquers, feel duty-bound to find something "wrong," but there have to be times that nothing is wrong, because the piece is in fact ready to send out. We submit our work knowing that an agent or editor will have revision notes for us, but the work is still the best we can make it at the moment, or we wouldn't send it out. Yet if we were to take that ready-to-go work to a critique group, they'd be "supposed" to find something wrong with it.
Maybe I'm just getting silly here, or maybe I'm easily tied in knots. :) How have you found critiquing either frustrating, helpful, or both?