"I'm not like most girls" — the key phrase of a "pick me" — the girl who wants to make herself look good to the opposite sex by pointing out how special she is. And this phrase aims to do this by elevating oneself above the standard for her gender.
When you're saying that you aren't like "most girls" as a way to express that you do something awesome, you're saying that you are superior to "girls" as a whole because of a certain behavior you engage in or don't engage in. You are putting your entire gender below you. This is explicit misogyny and it's not cool.
A lot of times, this behavior is accompanied by something that is geared towards impressing somebody of the opposite sex, and it will put down a cliché "feminine" trait or behavior.
"I'm not like most girls — I don't care if my man goes out and drinks without me."
"I'm not like most girls, I actually enjoy [insert sexual act]."
"I'm not like most girls; I don't need makeup to feel pretty."
So not only are you putting yourself above your entire gender to make yourself look good, you're trying to appear attractive to the opposite sex by appealing to the idea of misogyny… okay.
If you are somebody who prides yourself on things like this, great! I pride myself on a lot of things that make me a unique girl such as the fact that I'm so into cars. But it's not okay to ever let this become a moment where you believe that you are more worthy of something than another person, simply because of a quality you possess. My liking cars does not make me "different than most girls" — it just means that I like cars. It means that there's something unique that I'm interested in that I can connect with a lot of people about that I wouldn't normally otherwise.
If I let this turn into a thing where I'm proud of it because it's so different, I'm validating the idea that there are masculine and feminine behaviors, but I'm special because I am sooo above those gender roles. To further my example, if I bragged about how I'm such a cool girl because I like cars, I'm pointing out that it's abnormal for women to like cars. And I'm pointing out that I'm okay with this being standard, as long as I am somehow allowed to be admired for being the exception.
You are not allowed to put yourself above other people because your "sins" are different than theirs.
Stop being so conceited. Have enough self-confidence and humility to just be cool without trying to convince people that you're cool.