Why are alkyl halides used as solvents for relatively non polar compounds and not polar compounds? It is written in my textbook that :


  Alkyl halides are used as solvents for relatively non polar compounds.


Alkyl halides are themselves polar with carbon having delta positive charge and halide having delta negative charge. If polar compounds are dissolved in them, then there will be more interactions between the compound and alkyl halide. The polar compound should dissolve in it. 

What do they mean "relatively non polar compounds are soluble in alkyl halides" ? How will non polar compounds become soluble and why the textbook does not mention solubility of polar compounds?
Polarity is relative. Dipole moment (macro scale) and dielectric constant of the solvent (molecular scale)  are probably the most decisive. Water has &epsilon;~80, ethanol 25 and DCM is "only" 9. By comparison toluene, benzene or tertachlormethane have &epsilon;~2. The last example also illustrates why differences in electronegativity are not enough. Being symmetric (Td) tetrachloromethane has dipole moment of zero, even if there is a big difference between electronegativity of carbon on chlorine.