I’ll try and explain it as nicely as I can.
There was once an actress/singer over here, she’s was very good in her heyday but I think she’s retired now, anyway her husband did the dirty on her and went off with a younger women, the actress was livid and when asked by the press how she felt about it she said something like this “I’m not really surprised, T… (her husband) could never keep his Mickey in his trousers” That sentence stuck with her ever since, so now you know what it means or represents. But the word has always been used in Dublin since as far back as I can remember, when some of my UK cousins used to over and say ‘He’s taking the Mickey’ we’d be in fits of laughter as you could imagine. Funny how simple words differ from country to country.