Here is an easy to understand source (with graphics) of "Why heavy boats don't sink":
http://www.boatsafe.com/kids/021598kidsques.htm
Once you read the first paragraph on the link above - you will understand it really doesn't make any difference what a vessel is made of vs why it floats.
Large ships are made of steel mainly because steel is such a versatile construction material. It is strong, and can be easily cut, shaped, bent, wielded, and worked with.
Steel is really 'not' cheap. - it is in fact very expensive. . . It only becomes "inexpensive" when you consider what it saves in labor and other related costs when compared to using other materials. Pound for pound (for example) fiberglass would be cheaper, but your labor would be tremendously greater - which makes steel the much cheaper alternative for ship building.