Much of the confusion behind the meme stems from everyday misuse of historical terminology. In American English, men routinely refer to any bottled scent as "cologne." Historically and technically, that label refers to a specific, delicate category.
The original eau de cologne originated in 1709 in Cologne, Germany, concocted by an Italian expat named Giovanni Maria Farina. Farina wanted to recreate an Italian spring morning after the rain, blending bergamot, lemon, bitter orange, and cedar. Because French served as the dominant language of European commerce at the time, he marketed it using the French phrase eau de Cologne. Farina’s formula was ephemeral. It contained roughly 2% to 4% aromatic oils and faded within ninety minutes. People applied it liberally because it was never designed to project across an opera house.
Modern men's perfumes are completely different beasts. The bottles mocking victims of the "I wear cologne" joke are frequently Eau de Parfum (15, 20% concentration) or Extrait/Elixir grades (20, 40% concentration). When an untrained consumer treats an intense ambroxan-based elixir like an 18th-century splash cologne, the result is social suffocation. The nose rapidly undergoes olfactory fatigue, a biological process where the wearer stops smelling their own scent after fifteen minutes, while everyone else in the room suffers.