“Then the Pharisees went out and immediately plotted with the Herodians against Him, how they might destroy Him.” Mark 3:6
In Israel, in Jesus’ day, the Jews were divided politically into three different groups.
First there were the Pharisees. They were spiritually very legalistic and conservative. Culturally they were against any expression of identifying themselves with Rome. This would have been to accept their rule over them and that was unacceptable.
After this came the Sadducees. These were culturally in many ways still outwardly Jewish. Spiritually, however, they had abandoned some core beliefs, like the resurrection of the dead and the eternal reward of the righteous. They believed that the only rewards you would receive would be in this life and this resulted in a willingness to be selfish, grasping, and to be much more willing to adapt to Roman rule.
The Herodians, while still considering themselves Jewish, also thought that it was fine to see themselves as Romans as well. Religiously they could be very willing to compromise their beliefs. And culturally they had very much adapted themselves to the Roman way of living.
Generally, the Pharisees would have shunned the Herodians, see them as ritually unclean and traitors to the Jewish people, but when it came to Jesus they were willing to make an exception. Jesus was a danger big enough for these natural adversaries to decide to work together.
What had Jesus done? He had rejected the Pharisee’s traditions regarding the Sabbath and instead held to a simple obedience to the words of scripture. This could have probably been tolerated if Jesus had not also been very popular with the people. Multitudes followed him from all over Palestine. And in the towns and villages, it was no doubt being discussed, how he had reasoned more authoritatively from the scriptures than the scribes and Pharisees.
In short, pride and ambition fueled their hatred of Jesus. Right and wrong didn’t matter. It can still be that way today. Prophecy says it will happen again to those who seek to follow Christ. If it happened to Christ it’s good enough if it happens to us.