2D Quad Meshing is done on surface bodies. You have a been meshing a solid body. You need to work in SpaceClaim or DM to extract surface bodies from the faces of the solid body. In SC, that is very easy to do: select the face and type Ctrl-C then Ctrl-V.
After you have all the faces you need, you may need to do some editing to extend them to a common intersection point. Once that is complete, delete the solid body. Then you would turn on Shared Topology. That is very easy to do in SC: on the Workbench tab, click the Share button.