Ok, here's an update and an erratum :
Our previous answers, would still be correct if the question
were to ask why is graphite soft, but why is diamond hard.
Turns out that to completely melt graphite, you need to break
the intramolecular covalent bonds within the graphene
layers, as well as the van der Waals forces between the graphene
layers.
Still, this question is rather unfair, because this is still not
the full picture. Each C atom in graphite is sp2 hybridized and the
covalent bonds within the graphene layers is actually stronger (due
to partial double bond character) than the covalent bonds
within diamond.
So you have greater number of covalent bonds within diamond,
versus stronger covalent bonds within graphite. So who
wins? Turns out the melting points of diamond and graphite are
actually pretty close (despite graphite being soft and diamond
being ultra-hard).
So, yes we made a mistake in our assumption earlier,
but this is still not a fair question (so Cambridge
is also arguably at fault), because students (especially at
'O' levels) can't be expected to be aware of, and compare the
magnitude of energy required, to overcome the greater number of
covalent bonds in diamond, versus the stronger covalent bonds in
graphite.