Why use a GIF favicon? Is that for iPhone and iPad can read it?
<link rel="icon" href="/favicon.gif">
Browsers started supporting it. Also, ICO files are an old image file format for icons in Microsoft Windows. Since ICO is vendor specific, some choose to go with GIF.
Not to mention that there is an abundance of .gif editors, and few ICO editors.
After reviewing supported formats, your best bet is to go with PNG files if you are trying to get away from ICO.