"I'm merely pointing out that this is more akin to a debate scenario"

Ah, I understand better where you are coming from.

"You can't just say, well it's statistical data so you're probably wrong and then dismiss the claim."

That isn't what I was trying to do. I never meant to say that statistical data is likely wrong and therefore can be dismissed. What I was saying that proof usually has something more concrete than merely someone picking out a data set and then applying graphs that would seem to indicate what they believe is right. Trying to make a one factor correlation when things are much more complex multifactorial and interrelated things seems to me to likely to end up with false conclusions. I read recently that Statistics are like a Drunk seeking a lamppost for support rather than illumination. I found this to be a rather fitting synopsis.

My disputing the OP’s proof lies in the fact that it may likely be a misuse of statistics and therefore invalid. To support my supposition perhaps I was not very clear. It is the OP's position it would seem that more guns = fewer murders based upon the data set chosen. The OP further uses a statistical chart to make the point. So then, the central question becomes does this correlation actually exist or is it some brand of false causality.

From the Wiki:

When a statistical test shows a correlation between A and B, there are usually six possibilities:

A causes B.

B causes A.

A and B both partly cause each other.

A and B are both caused by a third factor, C.

B is caused by C which is correlated to A.

The observed correlation was due purely to chance.

Merely because one can find an apparent correlation in a random data set does not mean that the data set is a proof that the one thing leads to another. Since the supposed proof of the OP is based upon a simple 2 factor correlation then the fact that there are other options in interpretation means that the Proof is not really a Proof, but merely an interpretation which may or may not be valid. Certainly there can be no conclusion drawn from spurious correlation other than to point to the fact that further and more specific studies or data would need to be done regarding the question.

As an example of why this actually needs to further illumination I found these other ridiculous spurious correlations to illustrate my point.

http://www.tylervigen.com/

Things can be shown on charts which have no bearing on reality.