For example, they may put off calling their dissertation advisor to arrange an appointment to get feedback on their last chapter. Or more often, they fear finishing the draft of the chapter because it means handing it in and getting feedback. I've known numerous postdocs and professors who have not published as much as they might have otherwise, for the same sorts of reasons.
But what's the big deal? .... Yes, it does hurt to get criticism. And if there is unfair criticism, that's even worse, since the power imbalance in these kinds of situations may leave you feeling angry and disempowered.
You do have a choice about how you handle such situations. You have a choice in how you choose to interpret negative feedback and in how you choose to feel about it. If you knew that you would be able to talk yourself out of staying upset, no matter what the outcome, wouldn't it be better to just get the meeting over with? There's no point in dying a thousand deaths as opposed to finding out the news.
Believe in yourself. You're strong enough to handle this, or you wouldn't have come so far. As I said in yesterday's newsletter, avoid avoiding. It causes more pain than the feared situation itself.