That Mac OS X works more smoothly than Windows does not mean all Apps launch well without any problems. In this tutorial, we show the 2 effective steps to get rid of a circumstance that your Apple mail gets stuck on New Account Screen.
I had faced this Apple mail problems after upgrading to Yosemite 10.10, but i finally found the way to get rid of the issue. Let me illustrate the context:
From the Mail app screen, whenever you try to login with your email address (could be iCloud address or any other mail address), you get stuck at New Account Screen because the Mail app quits and take you back to the same screen as when you opened it up.
Hopefully this would help to solve your Apple mail problem.