I must be missing something about networking...
Every other time someone tries to explain networking, it comes across as "befriend people so you can take advantage of their resources."
It's not sincere to pick people to befriend solely due to what they have or who they know. It should be about who has similar values and who you get along with.
The way networking is described can lead one to believe that if you can't get certain people to like you despite your best efforts, then you don't deserve to succeed.