That would take the governor of Illinois to do, not the mayor of Chicago. But given that the sitting governor is no fan of Trump's, that's a definite possibility. Then again, Trump can just federalize the Guard like he did in California, so... that option is questionable.
The Guard under the governor's control would be separate and not under Trump's control. Guard vs Guard.
It's the same Guard. Same organization. The feds have the authority to activate them at the federal level. So you would have a National Guard in Illinois that would have to choose who to obey. Instant constitutional crisis. Not that we aren't already living through several.
Why not, then? Make them choose, and record those choices. It's about time someone chose to defend the Constitution, since the Armed Forces are unwilling to (betraying their oaths and the US in the process). This bullshit must end.
I don't necessarily disagree, but it's not really going to resolve much, it'll just add to the conflict.
I think, short of the military arresting Trump, we're beyond the point of non-conflict resolution to this Constitutional crisis.
You're probably right about that.