Why is diamond classified as an allotrope of carbon?
Because it is a possible structure that carbon can form into.
An allotrope is a structure that an element can form into.
Carbon can form different structures when compressed. First it forms coal, which is a fairly uneven structure, quite messy compared to the others.
Carbon can also form graphite, which is a very neatly layered structure that can be made into extremely thin, strong and conductive materials.
Diamond is made of more 3-dimensional molecules. Rather than being in neat layers alone, the layers are bonded together and form an even stronger but not conductive material. It is made only out of carbon, so is an allotrope of carbon.