Daft question really because it's like saying "why does This Woman fancy This Man". It's situationally dependent.
I've been an OW. I didn't chase him but having had that experience, I'd say the main benefit of a relationship with a married man is that you get all the good stuff with none of the downside. You get 100% of their attention when they are with you, lots of gifts, expensive weekends away in top drawer hotels, great sex and the excitement of a secret relationship. You don't have to deal with the day to day grind of a normal relationship - the kind of stuff women post about on here every day. Eg. bad habits, abusive treatment/unkind language, having to see dreadful in-laws, putting up with his boorish friends, seeing his skid marked underwear etc. It's like an ideal relationship frozen outside of reality - a fantasy I suppose. Personally, I wouldn't do it again and it was a one off for me but I totally see why some women would choose that type of relationship.
If you have no interest in having children and enjoy single life, that kind of relationship can work very well for the woman. It can work well for the man too - being totally compartmentalised. Plenty of relationships like this happen, run their course and the wife of the MM never finds out - so never gets hurt.
Other reasons would be
flirting with no intent just for fun and flattery (not serious chasing)
lonely or no other options (some married men are just after sex with anyone at all times and find unattractive, lonely women easy pickings - it's not that hard to manipulate people a little to get them to chase you)
sex or strong chemistry in a particular situation
the challenge or thrill of the chase
boredom and seeking some excitement
falling in love
(Also remember that what you "see" to be women chasing your friend may very well not be. You aren't with these people all the time and get one side of the story. For all you know, he is texting/flirting with them/ emailing them/ subtly placing a hand on the lower back/touching a knee etc etc offline. He could very well be encouraging it. I bet he is.)