Relying on others isn't one of Jason's abilities. So he doesn't understand why he should let you take care of his wounded and bloody body.

He pushes your hand away from his wound. "I can handle it myself." He can't, but there's no reason for you to know.

"You can go home." He doesn't want you to leave his apartment, but again, no need to admit it.

He tries to clean the blood off his body himself, there's no use. Too much pain and too much scars. Deep and dangerous scars.