This is not set in stone, and is my opinion. Now that that's been said, again, I personally think that being an adult is not about your age in numbers, but more about a level of maturity and your ability to handle situations.
If I get insulted by someone, how I react determines my level of maturity.
At primary school if I call Sarah a skank she would be very upset and run to the teacher and tell her I called her a nasty word. I would be called in and deny the crap out of it and get off with a warning.
Then in highschool if I called Sarah a skank she would either take offense and tell me I'm a huge douche and walk away, or find it really attractive and would follow me around like a loyal puppy. Either way the tattle tale part of her has left and she can now fend for herself.
But if you are out of school generally you learn to shrug it off and laugh at the person. This indicates that you have grown and are becoming an adult. Adults can take slurs and abuse as well as what they can dish it out. They also take responsibility for what they have done.
If I now call Sarah a skank and she calls her giant meat head boyfriend and tells him to pound me, it's what I deserved. But it also shows that Sarah is not confident in what she is and isn't. If someone calls me a squint I'll laugh at him, because I'm quite certain that I'm not squint.
If someone calls me a fag or a geek or a nerd or even fat I don't react because I am Ok with what I am. I know I love the ladies. I know I am a geek. I know I'm not a nerd, and yes there is a difference, and I know that I was fat, and that I'm not anymore.
I am secure. No matter what people say it doesn't affect me. So there you have it kids. If you are still insecure about who you are or take offense, it's Ok. One day you too shall be an adult.