Consider a member who is a leader for a given group.
Though the User Control Panel, that member can manage her/his group: in addition to the membership, the group leader can rename the group name, edit the group description, change the group type, change the username color, change the rank and also add or change the avatar.
The problem is the following: it's possible to add an avatar, or change the current avatar to another, but not to remove avatar (so that there is no associated avatar for the group). The option "delete image" doesn't work. There is a bug, even on proSilver (so, it's not a style-related issue).
The only way to remove the group avatar is delete it through the ACP, but only the administrators can do.