Why doesn't silica gel dissolve in ethyl acetate
Because (among other things) silica is not actually polar. Yes, theoretically a molecule of $\ce{SiO2}$ should have some degree of polarity to it. However, silica as a solid does not exist as single molecules.

Silica exists as a network of $\ce{Si}$ cations bonded together by $\ce{O}$ anions. One way of looking at it would be to say that each small bead of silica gel (or any other form of silica, glass or quartz) is one huge single molecule of silica.