"This Constitution, and the laws of the United States which shall be made in pursuance thereof; and all treaties made, or which shall be made, under the authority of the United States, shall be the supreme law of the land; and the judges in every state shall be bound thereby, anything in the Constitution or laws of any State to the contrary notwithstanding."
The citizens of the United States living in Texas are entitled to the privileges and immunities that flow from Article VI as well. If you want a new country, you need to find some new soil somewhere. And, as the Israelis can tell you, it's not easy nowadays.
But, again, the most important hurdle is that the people of Texas won't stand for it. Don't you believe that their feelings should count? Of course, you do.
The US Constitution is silent on the issue of secession. Get over it.
The constitution derives it's authority from the Declaration of Independence. The Declaration of Independence derives it's authority from God.
Acts of Man do not override rights from God.
Interesting that you would cite the example of Israel: Where do you suppose they found their "new soil?"
Right under their feet, as it happened.