"Menship" refers to the bond close male friends share. (Compare to "Femship") Friends is a broad term that can sometimes describe an acquaintance, a ride or die or anything in between. Menship indicates the depth of the relationship, and differentiates between a man and a guy who is a casual friend and a man and a guy who is his "brother from another mother".
It's an empowering term for men to publicly and proudly acknowledge their love and strong bond with the friend they consider "my boy" or "my man" without being overly vulnerable. (We know vulnerability can be hard.)
n. A character trait resulting from a blend of machismo, non-excessive masculinity, courage, and toughness. Manship represents the good side of manliness; a sort of bravery without braggadocio. Often contracted to "'ship"
The wide receiver showed some serious manship going up to make the catch and holding on to the ball despite taking a hit.