||I was coming here to make the same point. Consider the following heap:
If this is a min-heap, this violates the conditions as the root should always be less than its children. If we then swap the left child, we get
which still violates the property (root is still greater than its right child). If, however, we swap with the smallest child, we get
and the property holds. So in a min-heap, we should swap with the smallest child, and in a max-heap we should swap with the largest child.