Why is casein hydrophobic?
In milk, casein exists as a colloidal aggregate (casein micelle) with the properties you state, but purified casein is different. It is rich in proline (shown below), has no disulfide bridges, and hence little tertiary structure to hide the hydrophobic residues in the core of the protein with the hydrophilic residues on the surface to bind to water. In addition to having a hydrophobic side chain, proline stiffens the aminoacid backbone, hindering tertiary structure. The net effect is a molecule with too much exposed hydrophobicity to be water soluble. Casein micelles are complex structures and quite different from lipid micelles.

PROLINE