How does Pip feel he is a "gentleman" when he no longer has his money and what societal values is Dickens criticizing by calling attention to this?
Throughout the course of his young adulthood, Pip learns the real definition of gentleman. At first, he connects it with having money. A gentleman is a person of certain means and social class. This is how Pip is trained up to be a gentleman once he gets his expectations.
However, becoming a gentleman does not make Pip a better person. Actually, you could argue quite to the contrary. Pip becomes selfish, arrogant, and irresponsible once in London. He turns his back on his family, and in bettering himself he considers himself superior to them.
Once Pip finds out who his benefactor is, he is heartbroken. He realizes that the association does not elevate him at all.
“I have found out who my patron is. It is not a fortunate discovery, and is not likely ever to enrich me in reputation, station, fortune, anything. There are reasons why I must say no more of that. It is not my secret, but another's.” (Chapter XLIV)
Yet, a remarkable thing happens. Pip becomes a better person after discovering who his benefactor is. Once the blindfold is removed, he sees his situation for what it really is. He also stops looking at Magwitch as a criminal, and starts to appreciate him for who he is—kind of like Pip did in the churchyard. He becomes a son to Magwitch, a friend to Herbert, and a nephew to Joe. He even makes his peace with Miss Havisham and Estella.
The kindness Pip shows to Magwitch as he is dying demonstrates how he has changed.
“You always waits at the gate; don't you, dear boy?”
“Yes. Not to lose a moment of the time.”
“Thank'ee, dear boy, thank'ee. God bless you! You've never deserted me, dear boy.” (Chapter LVI)
It is not having money only that made Pip improve. It was having and then losing money that did it. Over time, Pip was able to step back and realize what he had been.