Why can't diamagnetic, and paramagnetic magnetize?
The concept of Ferromagnetism, Paramagnetism and Diamagnetism is completely different, though they all show magnetic properties.


FERROMAGNETISM: This is constituted of domain and each domain contains a large number of molecules (the number varies from material to material). These domains tends to align themshelves in a certain fashion in presence of magnetic field in order to achieve lowest energy and hence ferromagnetic materials show attraction to presence of magnets. Now these domains are not loose, but the arrangement can be made permanent in presence of some prolonged magnetic field. The amount of magnetism something can hold can be explained by hysteresis loop (NCERT Class 12 Physics Text Book). The arrangement of domains are shown below:
PARAMAGNETISM and DIAMAGNETISM depends on the number of unpaired electrons present in a system. The presence of unpaired electron to the system gives it a magnetic moment (given  by $\mu=\sqrt{n(n+1)}$, in Bohr Magenton , where n is the number of unpaired electrons). Hence the number of unpaired electrons, i.e. the excess number of electrons in the same spin, determines the magnetic moment. A material is called diamagnetic if the value of $\mu = 0$.


Thus paramagnetic materials are permanent magnets by their intrinsic property, but the magnetic moment is too weak to detect it physically. The increase or decrease in magnetic moment, or, the number of unpaired electrons in paramagnetic materials, is impossible by physical methods like keeping them in touch with magnet, or rubbing a magnet, or keeping it in strong magnetic field as done with ferromagnetic materials.

However, this is possible through chemical methods. For example, $\ce{[Fe(CO)6]^{3+}}$ is diamagnetic while $\ce{[Fe(H2O)6]^{3+}}$ is paramagnetic. However, this is not magnetizing, it is just changing what you are working with.