Actually on a purely military perspective, the odds were kind of on their favor. The post-world war II Royal Navy was designed and equipped to support the US Navy in the North Atlantic. More specifically, it was designed and equipped to help blockade and contain the Soviet Navy within the Greenland, Iceland and Northern UK gap, so that they could never reach the open Atlantic. So it was a Navy designed and equipped to operate close to home where it could resupply often.
Sending it to fight in the extreme South Atlantic stretched the Royal Navy and its logistics to the breaking point. With limited capacity to carry fuel, ammunition and supplies and a very small carrier air wing (the 2 British carriers were minuscule with less than 20 planes each), they had one shot and one shot only to retake the islands. If the first attempt failed, that was it. They would have to return home to resupply, refuel, repair and rest the crews.This process would take several months, which was more than enough time for Argentina to dig in , reinforce the island defenses and make it unconquerable. Also, it is unlikely that the British coffers could afford a second attempt.
Also, on paper at least, 1982 Argentina had a pretty formidable military, with modern and up to date aircraft, ships and submarines.
A British victory back in 1982 was not certain at all, and if the Argentina military had been half-competent, a British military defeat would have been almost certain.
The big question that bewildered a lot of people was: Even if they won, then what? After the euphoria and the jubilation of the victory passed, all the structural problems that destroyed the popularity of the junta would still be there, but Argentina would now be cut off from all Western powers. What then? Argentina would have been labeled a pariah by the Western powers and ostracized, leaving the USSR as the only alternative. Could anyone imagine Galtieri bending the knee to Leonid Brezhnev?