Consider the pairing obtained by taking each girl and assigning her to her least favorite stable partner.
Claim: The girl-pessimal pairing is a stable marriage, and it is the same as the marriage returned by MATCH.
This can be shown by the same type of argument as above or by appealing to the boy-optimality property of MATCH in the right way.
Now, if we reverse the roles of boys and girls (girls propose and boys tentatively accept), then we get a girl-optimal and boy-pessimal marriage.
