Some example sentences using each of the cases in Polish

This is not an answer at all, you are simply saying the same thing as me. You have given the rules, that is simple but why is this an exception in this particular case?

The accusative case, biernik, for masculine nouns, is divided into two categories: animate, and everything else; but this is only in the singular. In the plural, the division is between masculine personal (ie men and groups containing men), and everything else. So pies goes into the exceptional category animate in the singular, but into the everything else category in the plural. Dogs are animate but they are not men.

This is more to the point.