Anyone would feel very bad indeed if treated like that, especially if it stirred unpleasant memories. The next boss might be better, if not move on as soon as you can.

But surely the fault lies with the boss not with you. The best way of dealing with this is to say that while you welcome constructive criticism, you feel that his/her comments are not helping you, but that their guidance and advice would be welcome in private. Not an easy thing to do, but they would find it hard to say no. They may give helpful comments that you could discuss and accept in private, or they may just continue to be destructive. If the latter you would at least know to move on.