Did you know that the flags of El Salvador, Costa Rica, Honduras, Guatemala, and Nicaragua all use the same colors as the Argentine flag? That's not a coincidence! The "Belgrano colors", as they're sometimes known within anglophone vexillological circles, were first used on a flag by Argentine prócer Manuel Belgrano, inspired by those of Argentina's oldest national symbol, the escarapela or cockade.

The reason why the original escarapelas, light blue and white pins handed out to supporters of Argentine independence, bore those colors remains the subject of academic discussion. The folk tale I'm most partial to is that they represent the open sky, because that's the only thing the Spanish couldn't take from us¹.

Fast forward to the burgeoning Central American independence movement during the early 19th century. When these states, then united under the banner of the Federal Republic of Central America decided to seek independence, one of the few foreign corsarios, or privateers, that came to their aid was La Argentina, a ship commanded by Argentine naval hero Hipolito Bouchard. Bouchard, a fierce anti-monarchist liberal, has too many tall tales surrounding his name to recount here², but the important part is that in the process of helping the Central Americans fight back foreign aggression he planted within their territory a flag bearing the colors of the country that authorized his privateering, the Republic of Argentina. Inspired by this, and Argentina's then unbroken streak of military success, the Federal Republic adopted a flag bearing the same colors and a markedly similar composition.

When, after two successive civil wars, Central America splintered into the states we know today, all of them adopted designs based off of the FRCA's flag, itself based off of Argentina's, which is why so many of them bear blue and white tri-stripes to this day.

To answer some possible questions, the flag of Costa Rica seemingly doesn't follow this design because, in an attempt to seem more like France, they inserted a red stripe into the middle. Panama's flag has a different composition and colors because as a nation it doesn't trace its ancestry to the FRCA but rather to Colombia, which it was a part of before the US intervened to have it split off, which is why it bears colors strikingly similar to the stars and stripes.

¹This is very definitely untrue but it's also the explanation that feels the best.

²The most fun one is that he once landed on Hawai'i and made a deal with then ruling monarch Kamehameha I, which led to the Kingdom of Hawai'i being the "first country to recognize the Argentine state", this is disputed by historians but they're a bunch of nerds so who cares.