Both Michael and Burt share a sort of "loner mentality"
Michael has made it pretty clear that he doesn't really want to be in charge, but feels like he has to be. When something goes wrong and people die, he always places the blame on himself. He doesn't want the responsibility for everyone else but he also can't just leave everyone to fend for themselves. When the outbreak started, if Michael had his way he probably would have gone off on his own. It was only his sense of responsibility that forced him to go out, look for survivors, and then take charge of the situation.
Burt, on the other hand, is a survivalist type who doesn't seem to trust anyone but himself to be in charge. He doesn't want to trust someone else with life and death decisions so he tries to take charge and make them himself.
In the end I guess they both felt a need to take charge and inevitably butt heads when those needs clashed.
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