You could likely answer this in a lot of different ways since it's a heated topic that is largely opinion based. Consider that "states rights" was a major claim of those that supported segregation during the Civil Rights movement when they did not want to abide by federal regulation to desegregate. Consider some of the hottest topics of our time today: gay marriage, abortion, gun laws, the death penalty all face conversation about state vs. federal. I would suggest picking one or two topics and going into some depth on why a state could view the fed government as overly interfering. I've given some started ideas below, but all would need a bit more research to be a complete answer.
For example:
Marriage is largely regulated by the states and today only 13 states will issue marriage licenses to same-sex couples; however, the federal government recognizes same sex marriages, meaning same-sex couple receive the same benefits such as federal tax or death benefits that a male/female couple would. Should this be decided at the state level- many states think so.
Abortion:
Similar story- abortion clinics are mostly regulated by the state, but the federal government has increasingly expanded its regulations. There is a bill called FACE, which says there can be action taken if someone (or an entire state) prevents a woman from having access to an abortion, yet it can be very hard for abortion clinics to operate in some states.
Gun laws: Like marriages, licenses to sell guns are handed out at the state level, but federal gun laws prohibit the sales of certain types of guns arguably good, but limiting tax revenue for states.
A current hot topic is medical marijuana regulation. Currently several states have essentially legalized the sale of marijuana and so far the federal government has not interfered... but surely they are likely to soon. Recently, the house of reps voted to stop the federal gov't from interfering with states regulating marijuana, which was a big deal since the fed gov't previous position was that there was no identified medical use for pot.
For all of these- once the gov't has made a law, it has ways of forcing states to comply. This is often when you'll hear terms like "stepping on our state's rights." For example, they can withhold federal funding for everything from construction projects to job creation. They can also reward good behavior by creating incentives and funding to reach milestones- such as with the Clean Air Act.
