It's derived from a piece of dialog in a 1999 movie called "Fight Club." I've never seen it. Apparently it has a cult following.
In the late 1880s, a man known as "Snowflake Bentley" developed a technique for making beautiful photomicrographs of snowflakes. He made hundreds of photographs of snowflakes. No two were alike. This led to the idea that "no two snowflakes are alike." Therefore, snowflakes have come to symbolize uniqueness and individualism.
In the movie, a man tells a group of men, "Listen up, maggots. You are not special. You are not a beautiful or unique snowflake. You're the same decaying organic matter as everything else."
The derogatory term refers to people who believe that they (and everyone) are unique, special, and entitled to respect. They believe they are "snowflakes." So, it means "people who think of themselves as 'snowflakes' but don't deserve it."
Snowflakes are also fragile and delicate, so as an insult it also carries a connotation of people being weak or effete, not "tough."
Incidentally, I believe first in the 1990s, researchers found that the shapes of snowflakes are the direct result of the sequence of temperature and humidity changes they experience as they fall through cold air, and that snowflakes that fall together are visually identical. They have published photographs of pairs of snowflakes that look identical. A Google Images search on "photo of identical snowflakes" will turn up many of them.