"The logic of this statement escapes me!!"

The logic is that it (i.e. violence) is probably not getting worse (except in certain parts of the world such as Syria). Violence was much worse in the past - and not just in Texas 150 years ago. Many other cultures, in the past, had a much greater contempt for human life than we do now.

And by the way, as a Brit, it seems blindingly obvious to me that the US's problems with gun crime are largely the result of the ready availability of guns.