BUENOS AIRES—Argentina’s pro-business President Mauricio Macri is inviting low-cost airlines to invest in Argentina’s uncompetitive air-travel market, as long as they do something they do nowhere else: keep their prices high.

That caveat is baffling not only to the companies, but also to the many Argentines, like 61-year-old Luís Segato, who badly want to see more domestic flights in the world’s eighth-largest nation.

“Argentina...