Why is white phosphorus more reactive than red and black phosphorus?

White phosphorus is significantly more reactive than red or black phosphorus due to the structural strain inherent in its white phosphorus molecules.1

In white phosphorus, the atoms are arranged in tetrahedral $P_4$ units. This geometry forces the bond angles to be 60°, which deviates significantly from the preferred angles of 90°–109° found in more stable configurations. This "crowding" of covalent bonds creates a metastable, high-energy state that makes the substance chemically unstable and prone to vigorous reactions.1

In contrast, both red phosphorus and black phosphorus exist as polymeric structures where each phosphorus atom forms three single bonds that are spread apart sufficiently to be relatively strain-free. Because these forms lack the intense angular strain of the $P_4$ tetrahedron, they are significantly more inert and stable than the white modification.1