I have always assumed that the weakness of Oakhurst had to do with his decision to commit suicide rather than die slowly in the blizzard. But he also had a weakness for humanity, which he showed on more than one occasion during the story. As for being the strongest, he probably had a higher moral character than any of the rest of the outcasts, and he also seemed to be the most intelligent. Oakhurst was merely a gambler who had committed no other crime but playing cards in a town that looked down upon the sport. He was the leader of the group, and the others looked to him for guidance. In the end, he took the easy way out, dying alone so that the others might still have hope for a few more hours.