Trump v. Illinois is the kind of Supreme Court opinion written for the headlines. For example, the New York Times blared "Supreme Court Refuses to Allow National Guard Deployment in Chicago." Most people reading that headline might think that the Supreme Court struck down President Trump's exercise of executive power, or determined that there was no actual need to deploy the national guard. But none of that happened.
The actual basis of the decision has nothing to do with the President's Article II powers, or whether Trump properly found there was a valid basis to deploy the guard. The short per curiam ruling is at once narrow, yet extremely consequential. Indeed, the statutory argument the Court adopted was not advanced in the lower court by Illinois, but was raised in an eleventh hour amicus brief by Professor Marty Lederman.
In short, federal law empowers the President to federalize members of the National Guard if he is "unable with the regular forces to execute the laws of the United States." The Court finds that "regular forces" "likely refers to the regular forces of the United States military." The President did not point to any "source of authority that would allow the military to execute the laws in Illinois." Because the President has not done so, the President cannot show that those regular forces (the military) would be unable to execute the laws of the United States. QED.