Chakotay is captured by the Kazon, and his fate is tied to that of a tormented teenager. The Star Trek: Voyager Rewatch welcomes the late great Aron Eisenberg from the DS9 set to play that teenager going through “Initiations.”
And Eisenberg hits it out of the park here. He beautifully conveys the character’s adolescent turbulence, trying to balance the needs of his people with the fact that he very obviously doesn’t actually want to die, nor does he really want to kill Chakotay. But he’s trapped by the cultural mores of the Kazon. If he doesn’t kill Chakotay, his own sect will kill him. No other Kazon sect will take him in, and no one else in the Delta Quadrant will take in a Kazon.
We get a bit of Kazon history here to go with the cultural mores—which really are akin to that of street gangs, with initiation rituals and early indoctrination of youth—and their past enslavement by the Trabe has left them with a cultural distrust of uniforms and military order and such. So the option of coming on board Voyager is also rejected by Kar, because he finds the very idea of being on a Starfleet vessel repugnant.