Actually most people are not educated to tell the distinct difference between Strong/hardness and brittle/rigid.
Jerboy, when we are referring to the strongest, we mean in terms of strong/hardness. Best to explain through your example
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Carbon fiber material is stronger against spread out force than same thing made out of same weight of steel. >>
Carbon fibre is stronger because it's harder and it can take much more compressive force than steel, before
deformation(if it deforms at all). However because of its regidness of the structure, it's pretty brittle.
A good example is Glass, it's harder/stronger than iron but it can be shattered very easily, where as it's very hard to shatter iron because it's quite deformable.
Further details, read up around Young's Modulus and you will discover more
