This happens far too often both in dating and even friendships. I'll pursue a girl, who is pursuing another guy, who is in fact also pursuing a different girl. And most likely, that girls is pursuing another guy. And the endless pursuing of the pursuing leaves all parties unhappy, rejected, and feeling like crap. Sadly, that's a nature of dating and not much can be changed until two individuals are lucky enough to be pursuing each other.
I've witnessed this 'the pursuing pursuing the pursuing' in my own friendships. I've had people who want to be friends with me, who I don't care to be friends with. All the same time, I've reached out to other people who I wanted to be friends with, only to be rejected because they were busy reaching out to those they wanted to be friends with. What a head ache and how exhausting!
Friendships can be fulfilling by surrounding ourselves with those already around us. We need to stop the pursuing and look who's already in our lives. Many times I've had to stop myself from the destructive 'pursuing' behavior and go back and build and strengthen those friendships already around me. It's amazing how selflessness, service, and good hard effort can turn neglected or weak friendships into something so great and rewarding. Back to work.