When Richard Feynman refuses to explain how magnets work he fidgets and bounces and puffs in a way I recognise from a friend with long-term mental illness, who does this when he gets excited and gets really into explaining a topic. There are six such tunnels under the English Channel and the North Sea. There is a homunculus in your head and when you push your tongue up on the back of your mouth it tastes of lemon. Valve computers as crates of milk bottles. Electricity pylons as totem poles, across the United Kingdom.
The repulsion of magnets is the same as the repulsion you get when you push your hand against the sofa and it pushes back.
I really can't do a good job, any job, of explaining magnetic force in terms of something else you're more familiar with, because I don't understand it in terms of anything else you're more familiar with.