That's a question attributed to former Met Director Philippe de Montebello, in this Observer piece by Daniel Grant on the Met's new admission policy.
Jillian Steinhauer is at cnn.com arguing against the change, and at least tries to make the case that "the Met isn't quite like" all the other museums that charge for admission without anyone batting an eye. She mentions two differences. First, that the Met is "the largest art museum in the country." But I don't see what follows from that. Should the largest dance company in the country not charge for tickets? And where does this "largest must be free" rule come from? Why not "the top three must be free"? Or the top 10?
Second, she says "the Met is a public institution in many senses of the word." One sense she mentions is that "New York City owns its main building on Fifth Avenue and the land that building sits on in Central Park." But to the extent that matters, isn't it adequately dealt with by the fact that the museum remains free for New York City residents?
And the Philadelphia Inquirer runs an opinion piece headed "Museums should be free to everyone, regardless of where they live or how much they earn." That's a position I can at least understand. (I may not be convinced by it, but I can understand it.) What I don't understand is the position that this museum, alone among all the others, should be free.
UPDATE: 9 Works the Met Should Sell Right Now to Avoid Charging Tourists Forever.
UPDATE 2: More Than 200 U.S. Art Museums by Admission Price. (Spoiler alert: the great majority are not free.)