I have seen an interview with Justin Bieber, and there he said, “I just love the fact that what you do so brilliantly is you create such an amazing atmosphere for me,” and so I have a question. Why did he use "is you" and not just "you"
What Ethan Bolker said in his comment is absolutely correct, but may not quite answer your question.
The fundamental rule in English grammar is that a clause must contain a subject and a verb. Of course, a clause may, and usually does, contain more than those two elements.
One of the basic structures in English grammar is
Subject + (some form of the verb to be) + complement
The boy is tall
The boy is a student
In both examples above, the subject is the noun phrase "the boy," and the verb is "is." The complement in the first example is an adjective, "tall," and in the second example is a noun phrase, "a student."
Clear on the basic structure?
In your sentence, the words following "the fact" form a clause introduced by "that." The subject of that clause is the noun clause "what you do so brilliantly." OK. That is the subject. Now we need a verb. The verb chosen is "is." Now we need a complement. The complement here is the noun clause "[that] you create such an amazing atmosphere for me."
In other words, this is just a complicated version of the form
The boy is a student.
It is not good English to say
The boy a student.
We need a verb to join the subject and complement.