It has the power delegated to it by the Constitution, not the states, per the 10th Amendment.
Keeping this in mind, the answer to your question is simple: the mere fact that the states chose not to delegate expulsion authority to the federal government (and could certainly act to expel a state without its consent) does not effect the State's authority (not delegated to the federal government) to leave the Union.
But the Constitution does delegate the sole power to create states to Congress. By implication doesn't that mean Congress can also uncreate states?
And if you look at Article VII, then it appears that the states can. According to Article VII, ratification by 9 states was sufficient for adoption of the Constitution. So nine states could force the issue on the other four - ratify with us or take a hike. And if any of those states refused to ratify then they were out of the Union and out of the country. In effect expelled. So by rights it appears that states could be kicked out unilaterally. Right?
Ok, sure. Of course the States created the Constitution, but sure.
But the Constitution does delegate the sole power to create states to Congress. By implication doesn't that mean Congress can also uncreate states?
No. Congress is of limited powers, and if the power is not expressly granted by the Constitution, then Congress doesn't have that power.
And if you look at Article VII, then it appears that the states can.
Yes, as I mentioned on my last post, states can unilaterally expel other members. Congress, however, cannot.
I wish the US would kick out Texas. We would manage just fine.