Meaning of 'a third leg' [closed]
The "third leg" referred to in this case is an unnecessary object. We can walk quite well on two legs; we don't need a third (in fact, it might trip us up.) We don't need it at all.*
It's similar to another saying: "I need that like I need another hole in my head."
Elinor had had a passion for handsome men. The psychiatrist was handsome. "Mother" snorts at the idea that Elinor was seeing the psychiatrist because she needed psychiatric help (she obviously thinks she knows better.)
She had as much need for a psychiatrist as I have for a third leg.
*save for the person who needs a cane to walk, the proverbial 'third leg' in the 'evening' of a person's life.