The fibers are strong in both tension and compression (not equally so, see figure 1: http://home.iitk.ac.in/~mohite/axial_compressive.pdf http://home.iitk.ac.in

The fibers are strong in both tension and compression (not equally so, see figure 1: http://home.iitk.ac.in/~mohite/axial_compressive.pdf http://home.iitk.ac.in/~mohite/axial_compressive.pdf), but in compression their aspect ratio is very very very large so they buckle instantly… unless you glue them together so each strand is supporting the ones near it and the effective aspect ratio is much less. Aside from fiber wound pressure bottles just about any real world composite structure will experience bending forces which will put the top in compression and the bottom in tension. The designer might need to reinforce the compressive side more, depending on the application (e.g. if designing for stiffness the strength might end up with considerable margin for both tension and compression).