> Can someone explain how they thought taking over a state within the US would do anything?
There is no logical case to be made, but there is a strong emotional one.
People need to belong and have a sense of purpose. For years, these people have had NRA TV and the militia movements telling them that they and their guns are the only thing keeping America from being destroyed from within. That Patriots like them, who are willing to die for their beliefs, are the only thing that save America.
After armed militia members descended on the Michigan state house earlier this year and demanded to let into the the legislative chambers, not only was there no real consequences, but many people hailed them as heroes, with President Trump himself tweeting his support with "FREE MICHIGAN!!!!"
They were encouraged and supported at every point of their escalation, and now people want to pretend it came out of no where.
Just a group of lone wolves, who happened to be acting together.