Why is graphite softer than diamond if they are made up from the same covalently bonded carbon atoms?

Diamond is an extremely strong and rigid substance because of its molecular structure, which is giant covalent structure. This means that every carbon is covalently bonded to 4 other carbon molecules to form one big 3 dimensional structure, which is responsible for the hard and rigid properties of diamond. Graphite has a different molecular structure because each carbon only bonds to 3 other carbon atoms in a 2 dimensional hexaganol formation. These are covalent bonds just like in the diamond, so these flat structures are just as strong as diamond. Now, the part that makes the graphite softer than diamond is that the flat 'sheets' of carbon are bonded together by a much weaker bond than covalent bonds , called Van Der Waals forces. These are the bonds that break first to make graphite a soft substance.