No one likes being rejected. But we live in a culture where men make the first move. We don't live in a matriachrial society. Any man who has problems with asking a woman out has a problem that needs to be overcome somehow. And men get the chance to practice this unless they wimp out. Women are supposed to wait by the phone and play the passive role. That's a bit extreme but there is a logic to traditional male and female roles.
There are plenty of websites that discuss the fear of rejection and how it relates to fear of intimacy. Some people can't be objective about their own limitations.
I found more than these four...
Fear of intimacy is one of the biggest obstacles that must be faced within the context of community. Closely linked to its sister, "fear of rejection," it can result in failed relationships and the inability to relate in a meaningful way with other individuals.
http://www.allaboutlove.org/fear-of-intimacy-faq.htm
Fear of intimacy is at the heart of codependency.* We have a fear of intimacy because we have a fear of abandonment, betrayal, and rejection.
http://www.joy2meu.com/Fear_of_Intimacy.html
Fear of intimacy can be overcome only when the dread of rejection is removed.
http://matrimonyxpress.bharatmatrimo...n-be-overcome/
Finally, we can see fear of intimacy as a fear of rejection.
http://www.xyonline.net/MFI.shtml
It isn't a completely bad idea for a woman to make the first move as long as she understands the potential pitfalls of doing this.
I think it might be good for a woman to try asking a guy out at least once in her life so she can know what guys have to go through to get a date or a phone number.
If it scares you then go for it because facing your fears is empowering.