Why is the composite material stronger than it's constituent materials?

Answer 1

The fibers are extremely strong in tension, and have no strength at all in compression. The matrix (epoxy) has some strength in both tension and compression.

The bonding between the fibers and matrix allows force to be transmitted efficiently through the material, spreading the stress over a larger area.

So, the net result is that the composite material is somewhat better in tension that plain fibers, and a bit better in compression than plain epoxy.