The redcoats divided themselves into many groups of between 250 and 600 men depending on the objective at hand. They then launched many simultaneous attacks hoping to overwhelm the defenders, but found themselves charging head long at cannons packed with grapeshot (shrapnel). Many of the attacks floundered immediately and very quickly the redcoats had lost 2500 men either dead wounded or taken prisoner. By this stage the portenoes were firing down on them from every roof top from in front and behind them. the redcoats were trapped again. They finally had to plead for terms of surrender which were delivered to them written on the hide of a donkey. They finally had to leave Buenos Aires once more on condition that they sailed straight back to England.
In Buenos Aires jubilation turned to rebellion and 3 years later it would be the turn of the Spanish to flee. The Spanish fled in 1810 and the nation of Argentina was born. Part of the land signed over to the new Republic was the Malvinas Islands which the British know as the Falklands. Britain knew now that seizing Buenos Aires was out of the question but with naval superiority they knew they could size and hold the islands. And 23 years later in 1833 that's exactly what they did. But by this time the islands had and Argentine governor and a population, it was part of the sovereign territory of Argentina.
And that is why the Argentines feel very strongly that Las Malvinas Son Argentinas.