This is what I would like to tell people when I draw them. Given art history and certain iconographic art pieces people have certain expectations when it comes to portraiture and are often unhappy with the result. This stems from insecurity but also the belief that portraits are accurate portrayals of reality, like an artistic mirror of sorts. One of the reasons I enjoy portraiture is because you can do the exact opposite of that. The actual likeness of the person can be a jumping off point to ground the picture in some sense of reality, but after that anything goes. I particularly think it's important to draw the people around you, people who are close to you, or people who don't get any artistic attention on a daily basis. These are the people who matter most, possibly because it hasn't occurred to them that they matter at all. Without them there is no context for anything else.
Here is a semi-blind contour of my room mate Lily that I scribbled out one day in the kitchen. Disclaimer: she does not actually look like this in real life. Lily pens a delightful blog of her own where she muses about philosophy, films, fashion, and occasionally ... gay cowboys. Check it out here - The Petite Sophist.