Why do they call middle linebackers mike?

Answer 1

Identifying someone as the mike linebacker sets up the protection for the center and backs. Typically the offensive guards and tackles take the defensive tackles and ends (most offensive lines try to block big on big). The center and backs have to figure out who is left unaccounted for to block. So based on defensive formation and tendencies learned during film, the QB (or center) calls out the Mike, which gives the center his blocking assignment. Once the Mike is establsihed - it may not be the player who in reality is the middle linebacker, the backs will know who to block. Without doing this, the center and backs may be late in figuring out who their guy is.

Answer 2

It's just a nickname that shortens the calls at the line. The strong side linebacker is called Sam and the weak side is called Will.