NM tries to be smart about prefered/default connections and prefers wired over wireless. This is normally a good idea and sane default behaviour, but there are use cases where it make sense to prefer wireless connection. Such an use case is configuring a home router when staying connected to the internet through wireless, as I am doing now.

I found out that when I "create a new wired connection that is the same as the one I have already and then edit the connection and go to IPv4 Settings -> Routes -> "Use this connection only for resources on its network" and tick the box." (credit http://askubuntu.com/questions/89364/force-network-manager-to-use-wireless-for-an-internet-connection ), I can prefer wireless to wired. However, it is ultimately unobvious. It would be nice to provide some more sane UI to do this (a checkbox sayng "prefer this connection to other connections under Connect automatically?).