Sorry, it's just not that simple. Without the easy availability of guns and the resulting extraordinarily high number of suicides by gun in the US, it's possible the US suicide rate would drop.<quoted text>
Denmark proves you wrong. Lowest firearm fatality rate. Suicide rate still equal to U.S.
IOW - the US suicide rate may be artificially high because of the high success rate with guns and the high availability of guns.
Drawing the conclusion you have from one statistic alone isn't proof.