Solubility of a compound in a solvent, is not only a question of polarity but it is also a question of hydrophobicity/ lipophobicity, molecular affinity with the solvent, interactions between the molecules of the compound and the solvent, as well a question of some other factors.
Polarity is expressed by the dipole moment.
Hydrophobicity or lipophobicity (Lipophilicity or hydrophilicity in the inverse way) can be expressed by the partition coefficient (LogP). Generally, if LogP < 0 the compound is water-soluble and if LogP > 0, the compound is water-insoluble. But this is not an absolute rule.
Molecular affinity and compatibility are expressed by the solvent properties. Solvent properties can be estimated (often wrongly) either by the Hildebrand or by the Hansen method that are different approaches for the same issue.
Furthermore, some other factors like surface tension, anionic or cationic character, as well as formation of hydrogen bonds also play an important role, regarding solubility.
For solids, solubility is also a question of the melting point because the crystal lattice has to be destroyed during solvation.
I hope that I have helped you and not puzzled you. Be sure that until graduation you will have learned all these.
Besides, all above might seem complicated enough but there is a principle that simplifies all that to: “like dissolves like", meaning that solvents dissolve compound with similar physical (and chemical) properties.