There is a net magnetization (magnetic moment per unit volume) and it is anti-parallel to the external homogenous magnetic field; we say that the diamagnetic substance has a negative magnetic susceptibility. Also, when we talk about the atoms aligning with an external magnetic field and whatnot we are speaking of statistical averages; it is not necessarily true for each and every constituent of the substance due to things like thermal fluctuations. Finally, paired electrons cannot align parallel with an external magnetic field because of the Pauli exclusion principle; this is why paramagnetism is more prominent in substances wherein the atoms have an odd number of electrons.