It was a bureaucratic requirement with a psychological basis that was exploited to provide a looting opportunity for American soldiers.
Firstly, you have to understand that the Occupation authorities did not see peace as the complete objective. They wanted to "re-educate" the entire German population to become peaceful and non-warlike, the opposite of what was perceived as Prussian "militarism" responsible for the war. Millions of German survivors were forced into "re-education" and "de-nazification" programs of various types.
Part of the mentality of this effort was to outlaw all weapons of any kind to prevent even the thought of war. Just to give you a sense for it, English-speaking allied soldiers literally went through German libraries (the few that were not burnt down), removed any book they could find that had the word "krieg" in it, collected the books in piles and destroyed them1.
Allied soldiers who were participating in the occupation enthusiastically enforced these "no-weapons" rules, because antique firearms were interesting to them, and in many cases very valuable. The rule gave them the excuse to loot museums and private homes and seize antiques for their own collections. Many German antiques you see auctioned by Sotheby's or Christie's even today, including guns, are items looted from Germany during the war.
1. Read No Evil - Time Magazine