While I agree banning guns would affect the suicide rate little, if at all, firearms are the means of choice by a wide margin (45-70% depending on the region of the country): (
http://findarticles.com/p/articles/mi_m4021/is_n1_v20/ai_20111761 CDC Morbidity and Mortality Weekly Report).
I speculate the reason for the popularity of firearms is that death is essentially immediate, and final (if done properly), and guns are usually readily available. The only more peaceful means is by drug OD (which admits the possibility of discovery and resuscitation); however, suitable prescription drugs are not readily available. Other methods involve varying measures of horror and agony. Hanging is not benign. Even jumping from a high building leaves time for perhaps uncomfortable contemplation of one's decision.
There is another issue to consider. I have read many times that "suicide attempts" are a cry for help, and death is not intended. If a person choses a decisive method like a firearm, can this be an issue? Surely the person knows the result is final, and is not looking for help (except for a few that obviously botch the job, perhaps).
One can therefore argue that firearms offer a humane means of immediately ending life for the individual. Since people are going to commit suicide whether we approve or not, they should be permitted this means. Otherwise they will be forced to subject themselves to much more distasteful methods. Carrying a weapon is irrelevant: it is access that is key.
I believe that life AND death belong to the individual and society has no right to regulate suicide by regulating guns or anything else.
I agree with TallPine: your freind's opinion is fixed. Ask him the other reasons people should not be allowed to carry firearms: his reply should be illuminating.
Since Japan's high suicide rate was mentioned several times, I should point out that suicide (seppuku - ritual disembowelment by knife) is strongly embedded in Japanese culture, in part in association with a very rigid sense of honor. So I think Japan is a special case, even if most Japanese choose less ghastly means of death nowadays.
C