What is the criterion for saying, "So-and-so is my shaykh"?

There is no objection to a person saying "So-and-so is my shaykh" to someone from whom they have gained knowledge, even if that person is a peer or younger, out of reverence for knowledge and appreciation for its people. Indeed, the elders narrated from the younger in age or knowledge, and the Companions narrated from the Tabi'un, and vice-versa; to show that this is not an inversion of the isnad.