Professor McGonagall warns Harry against taking the advice of a painting, even if the painting is a portrait of Dumbledore.
"A head teacher's portrait is a memoir" (2.10.15) she says.
Harry, who is such a lazy parent that he'll use a map to monitor his own son, is too lazy to actually use that map to monitor his son, so he orders Headmistress McGonagall to do it.