In retrospect, the Falklands War seems like a spectacularly poor idea on the part of the Argentines, but at the time, the situation looked very favorable for Argentina. In fact, given the circumstances, it's a testament to the ingenuity and determination of the British that the war was as one-sided as it ended up being.
To start off, let's look at the RAF. The RAF in 1982 had plenty of modern aircraft equipped with far more capable weapons and systems than the Argentine air force (FAA) had at its disposal. Unfortunately for the RAF, their nearest base was at Ascension - 3,300 nmi from the Falklands. At such distances, only the longest-range strategic bombers in US or Soviet service had that kind of range under normal circumstances. The British did get around this through an elaborate arrangement of aerial refueling during the spectacularly impressive Black Buck raids, but everything about those missions were very much out of the norm. The Vulcans used in the Black Buck raids were pulled from the brink of retirement and hastily refitted with equipment for firing antiradiation missiles and a refueling probe, and the operation itself was absurd in its scope - to get a single bomber from Ascension to the Falklands and back, 15 refueling aircraft were used, fueling up the Vulcan a total of 7 times over the course of the mission. British naval aviation was better situated, but only because they were at least capable of putting combat aircraft within striking distance of the islands. The problem there was that the Sea Harrier, the only fixed-wing aircraft the Royal Navy had in service at the time, was a subsonic fighter, while the FAA had supersonic Mirage III fighters. Even with Hermes hastily pulled back from retirement, the Royal Navy had precious few aircraft and very little carrying capacity. The solution they came to was to hastily navalize a squadron of land-based Harrier G.R.3s and convert several naval auxiliaries to carry spare helicopters for the invasion.
On that note, take a look at the Royal Navy at the time. The Royal Navy in 1982 was suffering from a major draw-down of forces that was hitting the British military as a whole fairly hard. Fixed-wing naval aviation had been abandoned, and the British were in the process of retiring the carrier HMS Hermes to replace it with the smaller and significantly less capable Invincible class (of which there was only one available at the outbreak of war). When war broke out, the Royal Navy scrambled to bring into service as many ships as possible to support the expeditionary force, and it drew very heavily on comandeered civilian shipping. Among the civilian ships brought into service were three liners, five cargo ships, and fifteen tankers. The expedition was far removed from the operations the British were gearing up the Royal Navy to perform in the North Atlantic, and the expeditionary force was similar to the air operations in that it was very much a hastily thrown together force.
Compare that to the Argentine forces available at the time. The FAA had more fighters and attack aircraft at its disposal than the British expeditionary force (A-4 Skyhawks, Mirage IIIs, and IAI Daggers) and refueling capabilities that would allow them to operate from land bases away from the islands. Until the Black Buck raids caused the Argentines to withdraw their air forces away from the islands, the airport at Stanley was also capable of launching every jet in the Argentine inventory. At sea, Argentina had an aircraft carrier with a contingent of A-4s as well, and the French-made Super Etendard attack aircraft complete with modern Exocet anti-ship missiles. While the Argentine navy had plenty of dated ships in their inventory, the also had two British-made Type 42 destroyers that the British expeditionary force had four of, which allowed them to test tactics for attack against the very systems they expected to go up against.
So on paper, the situation in 1982 appeared to be very much in favor of Argentina. The British drawdown of military forces leading up to the war and remoteness of the islands made an expedition extremely straining on the British military, and the proximity of the islands to Argentina meant that the Argentines would be able to leverage logistical and in some areas equipment advantages over the British, as well as heavily fortifying the islands in preparation for any attempt to retake them. Given that and the mood of the British public at the time, it was felt that Argentina could make the remote, sparsely inhabited islands too prickly of a target for the British to be able to stomach the cost of retaking them.