Can't swap two columns in a Numbers table by clicking and dragging
If you have already tried clicking and dragging on a row/column header without any success, it might be because a cell in in the row/column you are trying to drag has been merged with a row or column which you aren't dragging (note: this cell may be hidden, and it still will not work). This will cause clicking and dragging to fail (without any feedback to hint that it is failing because of that reason).

This might have been why you were unable to switch rows.