Going all the way back to the Bill of Rights, leaders in the United States have valued states' rights. The Tenth Amendment reads:
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
The fear our nation's founders had of an over-powerful central government were understandable. After all, they were attempting to escape a monarchy. This tradition of support for states' rights persists today as many states within this nation attempt to be as separate as possible from the federal government (except when it comes to federal funding). Many political candidates speak of returning power to the states, and use the argument "it should be decided at the state" as a way to straddle the fence on issues ranging from marijuana, same-sex marriage, abortion, fracking, and countless others. Today, states' rights proponents seem less concerned with avoiding a tyrannical government than with the ability for a state to make it's own law when the federal government has made the "wrong" decision.
Yesterday, the Oklahoma legislature passed a bill making abortion illegal in the state. There's no reason to think the bill will be vetoed by the state's Governor, and Oklahoma will become the first state in the nation to criminalize abortion since Roe v. Wade. The implementation of this law would place Oklahoma directly at odds with the Supremacy Clause of the Constitution, which states:
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, any Thing [sic] in the Constitution or Laws of any State to the Contrary notwithstanding. (Article VI, Clause 2, US Constitution)
Under this clause of the Constitution, state's cannot pass laws in direct conflict with federal law. In the case of any conflict, the federal law will take priority. This means that Oklahoma, full stop, is in violation of federal law by passing a bill banning abortion except in cases where the safety of the mother is threatened. It would not be the first state to pass such a bill: North Carolina's bathroom bill, along with every state's legislation that has legalized marijuana, are in violation of the Supremacy Clause of the Constitution. So the fact that a state is in conflict with federal law is no sure guarantee that the feds will step in and enforce the Supremacy Clause.
Abortion is one issue that many argue should be "left to the states." In this case, people are not straddling the fence, but instead voicing their disagreement with the federal law and their desire for it to change. If the federal government passed a law making abortion illegal, would these same people be making the argument that it is a state's rights issue, and the federal government should stay out of it? Not so likely, especially with a subject as emotionally charged as abortion is. Most of those who say abortion should be a state's issue really just disagree with Roe v. Wade and want to be able to criminalize abortion anyway. Not speaking to the merits of this argument, it is less in the spirit of the Tenth Amendment and more about a desire to change federal law.
Another issue that commonly comes up as a states' issue is marijuana. In this case, claiming it's a states' issue allows libertarians to stay in the Republican party without scaring off the social conservatives. But upon further examination, it serves little benefit to view marijuana as a states' issue. For a parallel, look at the Temperance movement in the US. As individual states criminalized the drink, it didn't stop people from going over to the next state to purchase their booze, and it proved nigh impossible to prevent the illegal movement of alcohol into their states. The same dynamic is at play with respect to marijuana; the fact that the federal government has implicitly declared it a states' issue by not enforcing federal law means that access to marijuana across the country is increasing by the day. As time goes on, states who keep it illegal will be increasingly unable to enforce their laws. To be clear, individual states should not be legalizing marijuana; this should come from the federal government.
One more example of an area which many claim to be a states' issue: education. Politicians of all shapes and sizes trash the Department of Education, common core, and any federal standards or regulation with respect to education in the states. Upon looking at what some of these states do with respect to managing their individual education systems, their causes seems certainly less noble. In Texas, state control over education manifests itself in downplaying the role of slavery in the Civil War, banning the fact-checking of textbooks for potential errors (like referring to slaves as "workers), and skirting around the whole religion of Islam as a subject. The argument for state control of education is far less convincing when this is the kind of thing a state wants to do.
The founders of this nation incorporated many great ideas into the US Constitution. Some others sound nice in theory, but have played out far differently over the course of our nation's history. Going back to the Civil War, the Southern states argued for their right to maintain the institution of slavery. After World War II, Harry Truman's support of civil rights caused a schism claimed to be over...guess what? States' rights. The states' rights that were being argued for in this case were about the right to maintain segregation. The trumpet of states' rights has been regularly sounded during US history, but more often than not as a reason for states to drag their heels as the federal government attempted to push the country forward. To be sure, state governments do and ought continue to serve vital roles in the functioning of the country. When it comes to contentious issues such as those that are commonly argued to be about states' rights, in many cases the appeal to the Tenth Amendment is more a cover for the simpler argument that the state disagrees with the law the federal government has passed. In other cases, having different laws in different states creates a whole new set of problems.