There are ancillary things about being a Notre Dame man, such as enjoying a drink or two (or six), being a man of the world, and scoring with beautiful women (see my wife), but the most important are found in the motto above the door of the Basilica: "God, Country, Notre Dame." Ed Malloy fails in at least two of these areas:
God: A NDM needs to realize that the glory of God comes before everything else. This means that Notre Dame men are called to excel at everything they do, for God's glory, including academics, family, business, and football. We know that God has blessed us greatly, and we dare great things for His sake, in all our endeavors. Malloy has been willing to sacrifice the excellence of the university in football not for the glory of God, but for the cheap glory of the admiration of aspirational peers.
Notre Dame: A Notre Dame man loves the University that formed him with a love usually reserved for family. He sees it as his alma mater, the mother who nourished him. Since Notre Dame is named for the Mother of God, this is more than metaphor. A NDM would never promote himself at her expense. Malloy has, through his words to the media about the Willingham firing, attempted to inflate his own reputation at the cost of Notre Dame, the mother that nourished him. He attempts to inflate his own credentials in the pallid world of academia by declaring that he is embarrassed to be the president of Notre Dame.
Let's recall: he wasn't embarrassed by Kim Dunbar, by the rape trial, by the "sea of red" at the Nebraska game, by the age discrimination case, by the George O'Leary hiring, or by the airing of the Vagina Monologues on campus on Ash Wednesday, but he's embarrassed at the firing of an ineffective football coach.
Finally, a genuine son of Notre Dame knows that he is a part of a family, and that family disputes are best settled within the family. Malloy, by airing his grievance to ESPN, has acted like a jilted lover writing filthy things about his former beloved on bathroom walls.
Children, heed this tale. If you wish to be a genuine Notre Dame man, look at Ed Malloy, and do the opposite.