TL;DR: In context this is sarcasm: for ‘happiness’, read ‘unhappiness’.
At the start of Act I of Man and Superman, we learn that in his will, the late Mr Whitefield appointed Roebuck Ramsden and Jack Tanner guardians to his daughter Ann. Tanner does not relish this responsibility:
TANNER. It’s only too hideously true. Ramsden: get me out of it somehow. You don’t know Ann as well as I do. She’ll commit every crime a respectable woman can; and she’ll justify every one of them by saying that it was the wish of her guardians. She’ll put everything on us; and we shall have no more control over her than a couple of mice over a cat. […] She has the law on her side; she has popular sentiment on her side; she has plenty of money and no conscience. All she wants with me is to load up all her moral responsibilities on me, and do as she likes at the expense of my character. I can’t control her; and she can compromise me as much as she likes. I might as well be her husband.
He sees one way out of this unwanted duty, that is, for Ann to marry her suitor Octavius (whereupon the guardianship will be dissolved).
TANNER. Tavy: you must marry her after all and take her off my hands. And I had set my heart on saving you from her!
OCTAVIUS. Oh, Jack, you talk of saving me from my highest happiness.
TANNER. Yes, a lifetime of happiness. If it were only the first half hour’s happiness, Tavy, I would buy it for you with my last penny. But a lifetime of happiness! No man alive could bear it: it would be hell on earth.
It should be clear that ‘happiness’ here is sarcastic. Marriage is conventionally described as ‘happiness’, but Tanner predicts that a lifetime of marriage to Ann would actually be unbearable.
(This illustrates the importance of checking the original source. In the quoted passage from What's It All About?, Julian Baggini seems to have taken the quote from Man and Superman as if it were meant literally, something which he could surely not have done if he had read or seen the play.)
