A big thing with Wolverine's character over the years has been his role as mentor to younger X-Men, most notably teen-aged girls. In reading over the earliest issues of the "all new" X-Men (as they were called back in the day), it seems like the first hint of this role actually appeared with Kurt, to be refined later with Kitty. It wasn't in the almost parental form it later took with the girls, but the protectiveness, and trying to get a still young Kurt to accept himself and improve his abilities was already present. Jump forward twenty-five years, and it almost seems as though that role has been reversed, with Kurt being the mentor for Logan.
Instead of a mentor for survival, or age-related experience, Kurt seems almost to have fallen into the role as a mentor for being a man, as in someone with human compassion. When Logan had particular trouble with the beast within, who did he always turn to? Kurt. When he tried to make sense of his chaotic thoughts/feelings/actions, who did he ask for guidance? Kurt. I don't think Logan saw his friend in this role consciously- his pride probably wouldn't have let him - but it was there all the same. Maybe on some level, Kurt knew it, and that is why he never turned his back on Logan, no matter how angry he got. Just my theory.