You pick your friends
and you pick your nose
But you can't pick your friend's nose.
I am usually reminded of those days in grade school where you stand against a wall and people pick out teams for gym class. It's always uncomfortable to be one of the last to be picked. The same idea can be applied to being picked as a friend.
We are social creatures. Because of this we tend to socialize with others in a group. The reasons why we socialize may be infinite… however, who we pick to socialize with on a regular basis can be pretty finite and straightforward.
I like to think that people pick others for some quality that they have. For example, a shy person may pick a bold and social person to be with to gain confidence— likewise a helpful person may pick someone to whom they can help mold into a better person. You may also pick someone based on their physical characteristics (you only like blonds)— or socioeconomic status (I don't like rich snobs)… even though you may not want to admit it to yourself. People even pick for political (I don't date liberals)— or religious reasons as well (I will not marry outside my church).
I have found that some people only pick those people who will benefit themselves. If you have no purpose to them— they just are not interested in you. Also, if you no longer benefit them— they no longer have a need for you and drop you and no longer consider you their friend. One would think that people who use this cruel type of behavior would not have any friends want to pick them. However, it is quite the opposite— people for whatever reason are compelled to want to be these people's friend.
Perhaps those people who are more than willing to be anybody's friend are perceived as indecisive or weak, and therefore are not desired to be picked. So if you are a person who is restrictive and selective people will go out of their way to try and impress you so that you can pick them as their friend.