Korach started the argument for personal reasons. He wanted the job of nesius, he felt he deserved it, and the fight got notched up a few levels in the heat of the moment. Korach did not want to fight it alone and he found 250 other poor “victims” (victims of Korach’s persuasion I would suggest) to join him in his fight.
We are told nothing about these 250 people – other than of a select few. Why they joined Korach I have no idea, I can only assume he had powerful powers of persuasion, and maybe they did not like Moshe that much as it is. I do not know why they thought they deserved the position nor whether they believed they would win it when going up against 260 other people all claiming the same thing, with the possibility of death to the 259 or so losers. I am not sure what they were thinking.
It seems to me kind of pathetic that they joined the dispute at all and somehow it seems that they muist have been influenced by Korach, especially as it says Korach took them and rashi explains that to mean he took them in with his words. Korach convinced these guys they had a chance, when he knew they did not. I feel that might have been a worse offense than the dispute with Moshe. At least in the dispute with Moshe he had a possibly valid claim and wanted it verified. These guys had nothing and they were solely killed because Korach suckeres them into joining him, probably hoping they could force Moshe’s hand with their numbers.
Korach knew in advance that if anybody other than Aharon would win it would be him. We are told that he saw in a prophecy certain descendants of his. He took that to mean that he would be victorious, as he would clearly live if he was going to have descendants. He was mistaken because he did not realize his own children would back out of the dispute at the last minute. He knew these 250 or so people joining him had no chance. He knew it was either him or Aharon. Yet he still persuaded them to come join his fight. I find that despicable. He used them! And this was coming from someone who was one of the greatest people of the generation – he had nevuah, he was a leader, he was clearly persuasive and charismatic, we know he was learned and had the strength of mind and logic to make elephants jump through needles!!
When someone is trying to convince you to do something, check carefully to see what you will actually gain from the venture. See if he is using you for his own selfish purposes. Nobody, no matter how great they are, should be trusted automatically. Korach shows us that even the greatest of people can be looking out for their own interests and be willing to sacrifice innocent people to achieve their goals.