The marriage theorem says that if you have a set of of women and a set of men, for every subset of women A it has to be that set of connected man B is at least
$B \ge A$
All women are connected to at least one man in A.
The theorem can fail if you have for example one set 3 women on the other 3 men and two women only pick one man as their only choice, so therefore they cannot be married.
But how do find an infinite counter example and what would a picture look like.
I do not understand set theory very well so is there any simple way to show what an infinite counter example look like.
There is a transfinite version of the Marriage Theorem, proved using Rados's selection principle:
An infinite family of finite sets possesses a system of representatives iff the Hall condition holds for every finite subfamily.