Morning of the Sentence - Bleach Episode 51 Reaction

Infighting has begun because the execution is highly controversial, and there is also the murder of Captain Aizen on top of that which caused more infighting. Notice how many of the captains question the legitimacy of the execution (the normal punishment for Rukia's crime is not death). Soul Society is a single organization, but they are not one unified group. It is 13 independently led squads who just take orders from the same higher ups and work together when necessary. That being said, squads drawing their swords against one another is very illegal so it's not the norm.

So, in this moment you have captains like Kenpachi blatantly defying orders sent down by the head captain. In Kenpachi's case he is just a bit of a nutcase lol, it's not like he cares much about the execution. He would have probably killed all the ryoka if he thought they were a threat to squad 11 or just evil in general, but they were friendly to his squad so he ignored the orders to capture or kill them. Kenpachi wants to fight Ichigo again, so he decided to help them to better his chances of finding Ichigo.

Kenpachi broke the ryoka out of prison and was escorting them to the execution grounds, and on top of that he stood in the way of the two captains and their lieutenants preventing them from chasing the ryoka. That is treason. It would typically be punishable by death, which is why the other two captains drew their swords and intend to kill him as a traitor. Maybe they would have talked it out if it was a more respected captain, but the squads that unconditionally follow orders tend to hate or disapprove of Kenpachi as you will learn so they have no qualms about killing him if they have to.