What do you call a person who mocks, ridicules makes fun of you but can't take a joke on themselves? [closed]

What do you call a person who mocks, ridicules, makes fun of you at your expense in private or public but can't take a joke on themselves. The person would get angry at the slightest hint and probably start accusing you of this or that subconsciously using every defending mechanism (logical fallacies) that they can use.

I want to know to be able to communicate my feeling towards the person in question, without being too wordy and exhausting their willingness to listen. The person has previously been quite impatient of long explanations.

Solution 1:

The phrase that immediately came to my mind was that such a person can dish it out but can't take it.

Someone can dish it out but he or she can’t take it:

Someone easily criticizes other people but does not like it when other people criticize him or her:

He’s mad at me for teasing him – he can dish it out, but he can’t take it!

(Cambridge Dictionary)

For what it's worth, Cambridge Dictionary does specify that this is an American phrase, so I'm not sure if it would be recognized or understood in other regions.

Solution 2:

This sounds like a classic bully. Bullies torment their victims but crumble when confronted.

Solution 3:

There is an apt saying for people like this: -

People who live in glass houses shouldn't throw stones