Perhaps to avoid overtly saying “Japanese mafia” (yakuza)?
Or perhaps many moons ago someone who didn’t know better broke up the phrase into 反社会的 and 勢力, looked each term up in a dictionary (eijiro?), and came up with “anti-social” and “force”, then combined them into “anti-social forces”.
To be honest, I haven't been able to find the origin of the phrase.
For whatever reason, the term has stuck in Japan and even the respected Kenkyusha Online Dictionary lists the English as “anti-social forces”.
However, as has once again been demonstrated recently in the Olympus case, the term “anti-social forces” makes little sense to those outside Japan.
A quick Google search reveals that all instances of the term refer to Japan, or the English version of Japanese corporate websites:
Many news sources, qualify the phrase:
“…had indirect ties to "anti-social forces" -- a common euphemism for organised crime.”
“…Fujitsu now says he was warned about his dealings with "anti-social forces". The phrase is widely seen as a euphemism for organised crime.”
This site notes that it is “…a term used by Japanese law enforcement and regulatory agencies to refer to any group of criminals, including Japan’s yakuza.”
The fact that all overseas new articles clarify the term should be enough to make us sit and up and take note, since, despite the popularity of the phrase in Japan, it obviously has no currency outside of Japan.
This alone should encourage those who insist on using the term to stop and chose a different term, such as “organized crime”.
At present there are in fact no instances of “anti-social forces” on the Japanese Law Translation site.
While there are instances of the term on the Financial Services Agency website, at this point in time (i.e when there is no “official” translation in the Standard Legal Dictionary) when translating a legal document, especially one for use overseas, translators should not feel compelled to translate反社会的勢力 as “anti-social forces”, or should at least consider adding a translators note explaining exactly what the term refers to.
Incidentally, on the Japanese Law Translation site, 暴力団 has been translated as both “organized crime group” and “crime syndicate”, while 暴力団員 has been translated as “organized crime group member”, “crime syndicate member” and “member of a crime syndicate”.