Limiting registration to be only by Facebook, is it a good idea?

I'm building a web application which is available as a stand-alone website as well as a Facebook App, the target audience are mostly Facebook users.

However, I'm confused about the registration process: I want to promote my app! I want to publish updates from my web app to users' Facebook timelines (in a non-spammy manner) so that my app is auto-promoted among their connections, and therefore I need people to register in my application's facebook app and grant it permissions to post on their behalf. To ensure this, I tend to allow registration only by Facebook. i.e, no email registration, a registration is only possible if you click the "Login with Facebook" button and register through the Facebook App.

On the other hand, I myself hate logging with Facebook, whenever possible, I choose to register with my email address and not Facebook. And sometimes even I just don't register if there's no way to do that other than "with Facebook", is that only me or people tend to be like that?

If people hate "Login with Facebook" will that affect my app's UX? and will that drawback my app's promotion rather than help promoting it?

I need to hear your opinions. Existing examples (websites) are recommened.