In chapter 2 of Of Mice and Men, George tells the boss that Lennie got kicked in the head by a horse and that he and Lennie are cousins. Why does George volunteer the information?

Curley is being aggressive in this scene, his sense of manly toughness being threatened by Lennie's huge size and strength. Lennie is of course the opposite of what Curley believes, being a gentle giant who wishes no one any harm. Despite his impatience with Lennie, George cares about him a great deal and makes up facts to cover for him when Curley starts getting mean and even suggests he might not want them on as employees.
By saying they're cousins, George is putting off the impression that there might be something amiss about their relationship, since ranch workers typically travel alone. By saying they're cousins, this makes it seem less strange.
George also claims Lennie was hit in the head by a horse because this might sound better to Curley than just explaining that Lennie is mentally challenged. George is doing anything to make sure they get this job in the end.
The lies are also to protect Lennie from Curley's wrath. For all his bluster, George prizes his friendship with Lennie and feels responsible for him. Their strong bond is all that keeps the two men going through their dismal existence as migrant ranch workers.

George is worried because Lennie, who has a mental disability, can't answer Curley's questions well. George answers for him, which makes Curley angry. Also, Curley is suspicious of the friendship between George and Lennie. Curley says:




Well, I never seen one guy take so much trouble for another guy. I just like to know what your interest is.

To cover for Lennie, George tells the lie that Lennie was kicked in the head by a horse and that he's a cousin. George has just heard from Candy that Crooks was kicked by a horse, so the idea is on his mind.
Curley makes George very nervous. He is afraid Curley is going to try to fight with Lennie, because Lennie is big and Curley seems to want to prove he is tough. George is trying very hard to protect Lennie. He tells him to avoid Curley as much as he can, and he says to Lennie:







Look, Lennie! This here ain’t no setup. I’m scared.