Here, how about this: our 'rights' are not granted by the Constitution, they are emphasized, publicly proclaimed. The Constitution delineates the rights and responsibilities of the GOVERNMENT. Anything granted can be taken away.
For: Let's enumerate some rights, just in case future generations are stupidly literal about things and get confused because it's not all written down for them.
Against: Bad idea! By writing some down, we might create the impression that those are the ONLY rights.
For: Well then we'll make the 10th Amendment a catch-all, so it's crystal clear that rights exist beyond those we've enumerated so far.
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So did the 10th Amendment work? It seems like probably not, since people so frequently refer to the Bill of Rights as proof that the Constitution "grants" rights--rather than the intended effect, which is that the Bill of Rights limits government power over rights that already (and always) exist.
Why should the States have the rights to prevent the exercise of a citizens civil rights granted by the US Constitution?
The Constitiution, and the Bill of Rights explicitly, exists because there are things that are just not left up to 'the majority' to come to a democratic decision over. They are rights that were recognized to be inalienable rights. Time and again, courts have had to step in to once again assert that these rights already belong to all citizens because the States have used the democratic process to trample and curtail them even though the highest law of the land already should have put such questions to rest.
The Courts ruling says this. "the Equal Protection Clause, like the Due Process Clause, prohibits this unjustified infringement of the fundamental right to marry." Their dicision is not based on new law, it is simply stating that the US Constitution already recognized these rights.
Letting the States decide is letting the States pick and choose what parts of the Constitution they feel like following.