This is easy. If other states are going to waste everyone's time demanding a response from the executive branch on matters of secession, then I demand equal right to waste the executive branch's time on other trivial matters regarding states rights.
Sure, I could send petitions to my governor or state representative or member of Congress. Heck, I probably even should, since they'd have more authority to implement my change.
But the citizens of the great state of Pudding Town demand nothing less than the President of the United States taking time out of his busy day to say, "No. That's not my department. Talk to someone with that authority." Just like all the secessionists.
We also want pudding to be our official dessert. We like pudding.