Your fancy claws can’t cut what they can’t hit. An’ your hotsy-totsy healing factor… won’t save you… when I rip out your heart! 

Sabretooth

Wolverine and Sabertooth

The rivalry between Wolverine and Sabretooth is legendary in comics. It’s not always clear as to why these two are rivals exactly. That said it is likely that Sabretooth and Wolverine see each other as rival simply because they’re so similar. It also may be the result of their “animalistic” nature. There first encounter is traced back to Power Pack Vol 1 #27 and continued in Uncanny X-Men Vol 1 #212. Wolverine is searching for survivors after the massacre at the hands of Power Pack and Sabretooth. In the sewers their clash for the first time. At some point Wolverines healing powers gets nullified and Sabretooth thinks he can take advantage of it. He breaks his hand on Wolverines adamantium skull and is stabbed in the heart in return.

Why is that, Creed? You’re not my father, my brother, or my clone. Why is it we can never get rid of each other?

Wolverine

They’ve had numerous battles since. Often their fight are brutal and violent. The brutality is in part due to the fact that they both have violent fighting styles, a love of fighting and those fights are prolonged by both having healing factors. They were both in the Weapon X project and received training. In Wolverine Vol 3 #50-55, the rival comes to it’s end with Wolverine kills a feral Sabretooth, who is barely able to ask for Wolverine to end his suffering.