The discussion centers on the melting points of diamond and graphite, highlighting that diamond has a higher theoretical melting point (around 4300K) compared to graphite (approximately 3948K). However, graphite's melting point is often considered higher due to the partial double bond character of its C-C bonds, which makes them stronger and harder to break. Additionally, while diamond is fully covalently bonded, graphite has one free-moving electron and weaker Van der Waals forces between its layers, allowing them to slide past each other. The conversation also touches on the difficulty of measuring the melting point of graphite and clarifies that diamond does not melt under normal conditions but burns when exposed to high temperatures in the presence of oxygen. It is noted that diamond can theoretically be melted under extreme conditions, such as high pressure, but this is not achievable at standard temperatures and pressures.