No Girls on the Internet
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The phrase originates from the godawful Early Days of the Internet, where it was seen as the dominion of basement-dwelling, generally male nerds. Most of these have since migrated to /tg/, so the meme fits perfectly.
Interpretations
Memes, being living breathing documents, are constantly evolving. Consequently, 'No Girls on the Internet' has generated several interpretations during its evolution.
Dawn of the internet
This view is a literal interpretation and is considered the origin of the meme. Men are generally early adopters of any technology or social structure. As a result, the early days of the internet contained an extremely small number of women.
Vidya
As online games became more popular in the 90s, people began to discover that a good way to get free shit was to pretend to be female. Various idiots would give clan status, items, game currency, and other valuables to anything with a uterus in the hope that they would receive female attention. The meme evolved into a phrase to protect guildmates and friends from giving away their hard earned items to random fraudsters.
TITS or GTFO
This form of the meme is a result of the conflict of fraudsters existing during a time when larger and larger numbers of women were actually starting to use the internet. Unsure of whether a self proclaimed female was legitimate or not, people started to demand proof.
Final Form
As women entered online communities they began to exploit their possession of uteruses (uteri?) to give their posts and arguements greater weight in the eyes of retards. As a forum that despises identities, 4chan decided to fight back against the cancer of female shit posters that started every arguement with "Im a girl and i think that...." The result is one of the best posts ever made to 4chan.