Disagree with the current interpretation of the US constitution
The best way is if there are issues with the US constitution that itthe state firmly disagrees againstwith. Or, to be more specific, that there must beare issues with gun laws, medical laws andor voting laws that that specific state wants but the US supreme court demees uconstuntinaldeems unconstitutional. Or if it refuses to ratify bills imposed by the federal government and the supreme court orders it to do it anyway.
So, yeah, the supreme court has ruled it impossible to leave the union, so in the story it needs to be that court that your state antagonizes the most. The state in question wants theretheir own interpretation of the constitution and askasks the commonwealth for help. Because you can't use ceding from the union as a way to get out of debt - that won't fly with basically every other nation out there. And having backers to support your case in UN really helps, of course.