It would be better if you posted this as a notebook entry, so that people can make clearer feedback.

Either say: "Critics usually do not allow others to criticize them, even though they like to embarrass and criticize others." Or "A critic usually does not allow other to criticize him or her, even though he or she may like to criticize others." Criticism can make people angry or disappointed if they are not able to take the criticism simply. Therefore, if one of my friends always criticized me, I would respect his or her opinion and I would be cool. Or you can say "and I would be okay with it" instead of "and I would be cool".