Because he's Jewish.
So am I. I've been to all flavors of Jewish weddings and I do not recall ever seeing a groom (or anyone else) wear a tallis at one. I've been to a couple ultra-Orthodox weddings and the grooms there wore kittles and, of course, their tsitsis. (For those who don't know a kittle looks like a white lab coat and represents some sort of purity I think. Tsitsis are the tassel like things you might see hanging down near the waist of an Orthodox man, which aren't visible when a kittle is worn.)
So my question stands.
ML/NJ