How is Mel's discussion of love ironic?

Mel, a cardiologist, is talking as if he is an expert on love, on matters of the heart. As Nick, the narrator, says with ill-concealed irony,

My friend Mel McGinnis was talking. Mel McGinnis is a cardiologist, and sometimes that gives him the right.

And yet, despite his alleged expertise in the matter, Mel experienced an acrimonious divorce from his first wife, Marjorie. Mel thinks he can illustrate the meaning of true love by an anecdote about an old man and his wife he treated in the hospital after they had been in a near-fatal car accident. However, his recounting of the story is punctuated by persistent bickering with his current wife, Terri. We sense that all is not well in the marriage, making Mel's claim to know the true meaning of love all the more ironic.
Furthermore, Mel heaps scorn on the idea that Terri's ex-husband Ed was motivated by love for her when he committed suicide. At the same time, however, he is so lacking in self-awareness that he fails to see the parallel between his own anger at Terri and the physical violence that Ed often displayed toward her. As Mel believes that love is purely spiritual, he is unable to acknowledge that it can also be displayed through actions and words.