He explains it in his "Angry Warrior" story in "Resolutions".
He was looking for a woman to take on his burdens so he wouldn't have to be angry anymore. By him finding Janeway and getting them stuck in the DQ, made all his problems go away because now all the problems became hers.
In other words, Chakotay was a lazy deadbeat that was going to make his woman work while he stayed home and picked his ass all day.
Seriously, I don't see why J/Cers wanted Janeway to hook up with such a no good nothing of a man as Chakotay.
Janeway couldn't castrate a man that never had any balls to begin with.