chair's leg or leg of the chair. two tomato fields or two fields of tomato. Isn't it right that we use ......'s for living things and ..... of ....... for non living things
No because in that case you wouldn't be able to say a group of people/animals or Henry's chair.
Have I misunderstood your comment or you are repeating what i am saying. I am relying on memory here. For group noun we use 'flock of' or 'school of' or pride of'. For any living thing we use, such as you pointed out, Henry's chair, elephant's legs etc.