“He that desires peace must prepare for war” is a double entendre. Being prepared for war is the only way to assure peace, and if you wish peace through abandoning the ability to make war, in the end you will need to fight a war.
Britain’s claim to the Falklands dates back to the 1600s, but the French where there first.
Argentina occupied the islands from December 1832 to January 1833 while it was unoccupied. The islands were promptly retaken by the British and this short occupation is the basis for Argentina’s claim.