OK, here goes my try at it. The Court didn't argue this on 2nd Amendment grounds, and here is why...
When the Second Amendment was written, it absolutely did not apply to the states. The Bill of Rights was a guarantee that the federal government and only the federal government would not oppress the citizens' rights. To illustrate, the First bars establishment of an official religion. However, up through the 1820s, some states had established religions. Barron v. Baltimore upheld the restriction on the BoR to the fed. gov't in 1833.
This was not Alito's argument in the case. He looked at the 14th Amendment, which absolutely applies to the states. (The 14th has a sordid history toward ratification that makes anything Obama has done look like a child's game.) The 14th is the giant tunnel in the Constitution that brings prohibitions on the federal government to the states. This didn't happen till something like 1925, though, in Gitlow v. New York.
The 14th gives you due process rights. Actually, it gave former slaves due process rights, as it was intended. The Supreme Court has used this to give you "abortion rights" as well as now gun rights. Alito and Thomas were a bit crafty about it, though. They spoke in the decision about the due process rights of former slaves to own guns. If a former slave could own guns, how would it be fair to restrict you?
I read parts of the argument and I was dubious at first, but I think the reasonings of Alito and Thomas (his is a bit different) are interesting. Apparently Scalia had some disagreements, but I haven't read those.
From my perspective, being able to defend yourself is a matter of Natural Law, a God-given right. Any law which denies self-defense is itself illegal. I'm a strong believer in state and local rights, though. If a community wants to ban guns, should they be able to do so? Not by Natural Law, but I'm uncomfortable with federal involvement.
I'm a very staunch supporter of gun ownership with very few restrictions, but personal feelings should have nothing to do with the law. I need to read this case in more depth because the arguments are not simple, and the decision is very lengthy.
Justice Thomas' decision was more than a bit different. He avoided the Due Process argument and used the Privileges and Immunities clause.
"I agree with that description of the right. But I cannot agree that it is enforceable against the States through a clause that speaks only to process. Instead, the right to keep and bear arms is a privilege of American citizenship that applies to the States through the Fourteenth Amendments Privileges or Immunities Clause."
Why would the 14th even have been needed if recently freed blacks became 'people' rather than slaves? Wouldn't the BOR apply to them at such time? Oh, that's right, the BOR only limits the federal government.
This is where I don't follow the argument. I believe that certain items were put there as a 'for the record' statement with the understanding that no government could infringe on the RKBA, for example, as it would now be enshrined in a document with the most supreme legal status.
I think they might have done the same with 'ownership of humans' had the issue been settled at the time of it's writing. The same for fetuses- had they imagined a million a year would someday end up in dumpsters.
To me, the constitution was to be the document of all documents, attempting to encompass as many freedoms as possible while assigning as few powers as necessary to the general government. Ammendments allowed the states a way to fine-tune the sucker.
In that light, no person's right to keep and bear arms may be infringed as many states are currently guilty of with fees, licenses, and permits, etc. However, the states might weigh-in on the What, Where, When, How, and How Much with regards to 'arms' while being forbidden from denying a right to keep and bear them.
The way this is going it'll be ages before this 'right' is enjoyed as intended, imo. Any right that cannot be exercised is not a right at all but more likely a priviledge. I still haven't come across the Bill of Priviledges. I bet there are at least four justices who have a copy though.