Android and Google contact sync: "Starred in Android"
"Starred in Android" is a special group. You don't add a person to the group through the groups interface, but by tapping the little star on the contact profile on your phone. That sorts them to the top of the "favorites" list.

There's no concept of a starred contact on the web app side, so I guess they decided to create this special group. (In fact, from what I recall, this group won't be created until you actually "star" a contact.)

So, don't scroll to the bottom of your contact to try to add them to the "Starred in Android" group. Scroll to the top and tap the star.