"why aren't the gun homicide rates higher in the United States than Mexico?"
Mexico has vast lawless areas where there is nary any law enforcement, and cartels fight with other cartels for power.
For reference:
+ Canada has many fewer guns than the US, and many fewer gun crimes
+ European countries have vastly fewer guns, vastly less gun crime
+ Japan has almost no guns, and almost no gun crime.
When looking at civilized states where laws are actually enforced then there's a correlation between guns and gun crime.
While most legal gun owners are not more likely to be criminal, the preponderance of available guns just gives the statistical chance that someone in a bad mood can get one much higher.
In other words: loose gun laws mean low level bad guys can get a hold of guns in a much more easy way.
Every car you pass on the highway in the US, there's a half decent chance there's a gun in there. In Canada, there's very little chance.
The 'odd man out' is Switzerland: they have a lot of guns. Their guns are however for civil defence: rifles, not hand guns, and they definitely do not have 'self defence culture' whereby people actually carry weapons. They are locked up in the basement or at the armoury. Also, they are amazingly civilized with low social strife etc..
It would be nice to see America have much stricter gun laws while not so much infringing on the essential right to own a gun. I think it's possible.