I shudder to think of them doing that during covid...
Sharing mate is a ritual too culturally rooted to Argentinian society. It's hard to explain but it goes beyond drinking a hot beverage.
Mate is a social thing here. You're supposed to share and there's a ritual about how the round goes, who prepares the mate for the rest of the group, and how you signal that you don't want to drink anymore.
Also curious: Uruguayans share our love of mate but for them it's an individual thing, they don't share their mates. So we say that Uruguayans are born with a mate thermos under their armpits, one for each of them!
Mate is traditionally drank with a metal straw, a small "cup" (the gourd) and a bottle with hot water, which we Argies always call a "termo" (after the thermos brand, much like many people call tissue paper "kleenex"). This bottle is used to constantly refill the gourd, since each "serving" of water only lasts a couple of sips. Note the yerba mate inside the gourd lasts many rounds of sipping until it also needs to be changed.
So to drink mate in Argentina, you need yerba, one straw, one gourd, and one termo per group of people, because we share the mate. But Uruguayans don't share their mate, even though they are heavy mate drinkers, so each carries their own mate and termo under their arm, everywhere. Hence, "they are born with a termo under their arm".
It's not really a joke, more like a friendly description of Uruguayans and mate.