HI Mala,

re:
> Why can't this structure be extruded?

Extrude works on either curves or single surfaces (or also on faces selected on a solid which will automatically boolean with the solid).

Your object is neither of those, it is a "joined surface" made up of 2 surfaces joined together.

To extrude it, select it and run Edit > Separate. Then select the 2 surfaces and run Construct > Extrude.

Since the surfaces are not planar it will default to extruding in the z axis direction which would make a degenerate object so you will need to use the "Set dir" option and pick 2 points to define a valid extrusion direction.

Also note that if you want a result that has uniform thickness you should use Construct > Offset > Shell instead of Extrude. You don't need to separate it first if using Shell.

- Michael