My visceral opposition to strong states' rights comes from a variety of sources. First, I don't like the way my state generally does things. Utah is a drag. This is an intellectually shallow argument against states' rights, but its real for many people.
Second, I think the constitutional arguments behind it are pretty weak, or have become weaker in a changing world that the Founding Fathers could not possibly have foreseen. I went into detail about this here.
Third, I think there are certain basic privileges and protections that the federal government should ensure that many states are hostile to, such as health care, which we'll discuss more below. I support the federal government setting minimum standards for health care, the financial sector, etc. that are binding on states and put all Americans on a more equal footing. As long as we are the United States of America, what's bad for one of us is bad for all of us.
Fourth, I distrust corporations more than government and think corporations have too much power, and decentralizing their main counterweight, the federal government, strikes me as a way to strengthen corporations and allow them to run amok (think Gilded Age abuses and oppression, and go read The Jungle by Upton Sinclair).
Fifth, and related to the previous two points, is the threat of a race to the bottom. This occurs where, in economic competition, competing political entities will race to deregulate and dismantle consumer protections in an effort to attract businesses. Wal-mart, for instance, is not going to be relocating its headquarters to a state with strong union laws on the books.
Sixth, the history of states' rights isn't exactly inspiring. States' rights has been synonymous with slavery, Jim Crow, anti-segregation, and a whole slew of civil rights atrocities. The latest incarnation is for certain states to take an incredibly hostile view towards immigrants, which I find despicable and not very Christian. Certain states don't seem to be able to mind themselves when it comes to civil rights and it just won't due for them to drag us all down to their level.
Finally, conservatives have ruined the issue for me by attaching it to their social agenda and supporting states' rights when it suits them (abortion, immigration) and opposing it when it doesn't (drug control, gay marriage). There are actually hardly any people anywhere on the political spectrum with a consistent stance on states' rights and I therefore find it hard to get on board.
Despite all of this, I can't help but agree with the famous line from Justice Brandeis that, "It is one of the happy incidents of the federal system that a single courageous State may, if its citizens choose, serve as a laboratory; and try novel social and economic experiments without risk to the rest of the country." The individual states as laboratories of democracy is an appealing metaphor that works on many levels. I like the idea of states being courageous and searching for new, progressive solutions to our problems. But it only works if states find themselves out ahead of nation as a whole as opposed to falling behind, and if the state doesn't have an elevated stature above the others in a certain area.
For example, New York and Delaware hold the keys to the corporate and financial engine of the nation. If they aren't out ahead of rest of us in governing corporations and banks and protecting consumers, then the whole nation suffers. So when they dropped the ball and the nation slunk into the Great Recession, the federal government had to step in and try to fix things. It would have been better if those states had taken the lead and reformed the financial system before disaster struck, but they didn't and that's why we have the feds to step in and clean up their mess.
It became clear many years ago that there was a serious problem with the health care industry. Tens of millions of Americans couldn't get coverage, coverage wasn't portable which tied people to their crappy jobs, and those with coverage were facing rising premiums greatly outpacing inflation with benefits falling by the wayside. If various states had taken this seriously and fired up their bunsen burners and tried to find real solutions perhaps the federal government would not have had to play such a heavy hand. The one state that did, Massachusetts, became the basis for the federal reform. But otherwise they didn't. But now they are.
Vermont is about to create a single-payer system. California and Oregon have progressive systems aimed and covering all residents. This is good, and could be the beginning of real health reform in the country. The states should be out in front, and when they are the whole federalism system works better. Unfortunately, that race to the bottom almost always means that they are not, and that is why it is too risky to put too much faith in states' rights, for now anyway.