thats not an italian flag... its hungary.
It's also not the flag of Hungary. Each country has specific protocols for how their flag is supposed to be displayed. Whether or not it's actually followed is a different point entirely.
The most general case would be to rotate a flag 90 degrees clockwise and then flip it around, with some countries not flipping it at all. Countries like the UK have also special rules for when the pole is on the left/right, with the general case in the UK being a simple 90 degree clockwise rotation.
There are no national flags that are displayed vertically with green, white, then red vertical stripes. Hungary would be red, white, then green, with different shades.
In universe, you could explain it as the staff not knowing anything and thinking that every country is like the UK with a simply 90 degree rotation (it's actually more complicated than that), with the US being different just because "Americans like to be different", but then you're left wondering about countries like IND/RSA/CZE, where the dev had the flags displayed correctly. In the cases of ARG/BRA, you have to wonder why the school went looking specifically for vertical versions of the flags (and I'm not even sure they're correct). You also have headscratchers like BEL/ITA/FRA, where you are left wondering where they even found such a flag. You could plausibly explain it as some extended versions of the flags (think of the ones that look like vertical scrolls/banners), but that wouldn't explain why the staff thought it was appropriate to combine them with other flags. I don't think it's necessary for me to write about why the CAN/ESP flags are wrong, they speak for themselves.
Out of universe, the answer is simple - the dev thinks he's smarter/more cultured than he actually is. It's actually pretty funny.