Is misandry is real?

Not really. It depends on how accurately you are defining your terms.

If misogyny is the hatred of women and misandry is the opposite (hatred of men) then sorta.

However, misogyny is the systematic, institutionalized, and societally supported hatred of women. And the opposite of that cannot exist because it was created and is reinforced by men.

(All of this with the assumption of a gender binary for simplification)

~Dina