Although you can have a relative pronoun, it would be more natural to say ...the man he used to be.
Perhaps the teacher thinks that is better than who because the sentence really means the kind of man and not simply the man as in That's the man who came. I don't think there's much difference.
The Google Books Ngram Viewer has something interesting to say about "the man  he used to be".
The Viewer is limited to a string of 5 words, so I searched for "man he used to,man who he used to,man that he used to"
—assuming that "the" is the likely preceding word, and "be" the likely following word.
"No relative pronoun" is by far the most frequent; "that" is weakly in second place; and "who" appears never.
If you remember the Beatles' song "Yesterday", you've heard Paul McCartney sing "I'm not half the man I used to be."