Why shouldn't they be allowed to secede? Let the inhabitants of each state vote under international supervision to make sure the vote goes by according to western standards. I see no reason why any community should be barred from seeking independence and self rule.
Because that's not how a functional society works. If Texas wanted to secede from the USA the whole USA would have to be called in this decision. You can't do what Puidgemont did in Catalunya, call for a referendum in the specific region, count the votes and declare independence from the central government. You are part of the government, if you want to secede this must be a common choice.
If you were an adult you might understand this with a (non-perfect) similitude with divorce: you cannot divorce by yourself, you need to sign the documents as a couple for divorce to take place.
That's also why Russia's claim of annexation of the Ukrainian regions has no value for the international law, it's a faux secession with no bearing on the Ukrainian national rights
Something tells me the secessionists wouldn't agree with that. Are they going to let their urban centers secede from their states if they voted to do so?
If Texas secedes from the US, does Houston get to secede from Texas?
You'd end up with a situation like Brexit, where Scotland voted to stay but had to leave with England, only the whole thing would be 100x worse because US states are far more integrated than EU member states.