Now i know why. IE cant be used as your default email client. It is a browser and Default Applications can only be used for such things. The system doesnt know that you use webmail nor does it know the website your trying to use. You cant set it up to open specifically just that website to use your email. As it would just open IE and its default page.
You will have to force it by specifically selecting the file type in the "Associate a file type or protocol with a program". You wont be able to use any built in settings within IE or Firefox cause they dont understand that you want to use the browser. Like stated above, they dont recognize the browser as a accepted program. You will have to find the .eml extension and force it to associate with IE.
So really there is no way to specifically tie the emails to a browser. You can force it, but that doesnt guarantee that when you click a email link that it will open IE. It may just seem like it is working then do nothing. Cause the file association is forced to a program it doesnt recognize to be proper for that type of file.