Why is the ground state electron configuration for Lithium $1s^{2}2s$ ?

The electronic ground state for Lithium is $1s^{2}2s$, and not $1s^{2}2p$. The traditional argument for why this is so is based on a screening argument that claims that the $2p$ electron is better shielded by the $1s$ electrons, and therefore higher in energy then the configuration that includes the $2s$ electron. We show that this argument is flawed, and in fact the actual reason for the ordering is because the electron-electron interaction energy is higher for the $2p-1s$ repulsion than it is for the $2s-1s$ repulsion.