For anyone wondering what this is

Bertrand Russell coined an analogy: for any (even infinite) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate collection (i.e. set) of shoes; this makes it possible to define a choice function directly.

For an infinite collection of pairs of socks (assumed to have no distinguishing features such as being a left sock rather than a right sock), there is no obvious way to make a function that forms a set out of selecting one sock from each pair without invoking the axiom of choice

So mathematicians always make the assumption that they can make a set from an infinite list of other non-empty sets based on this hunch, rather than any concrete choice function. And then they build mansions on top of this foundation, and use it to score chicks and ferraris, smh