So yes: I am also very thankful that I had the opportunity to learn a social couple dance (with 'social' meaning non-competitive and without fixed dance-partners)
The first lessons were hard and sometimes frustrating when you don't make progress as fast as you want to. But for me it paid out and changed my life. Today I go dancing twice or more a week. No matter how stressed I am after work: I always come home from dancing relaxed and smiling.
When dancing you have to deal with a multitude of things in parallel:
1) You listen to the music carefully and match your body movement to it.
2) You are creative and come up with figures/movements fitting the music in realtime (you cannot plan too much into the future)
3) You constantly "read" your partner: You only have fractions of a second to feel his/her center of mass, anticipate her/his possible future movements and react accordingly. Blindly forcing your partner into movements he/she can currently not execute (for example due to having the weight on the "wrong" foot) will not work.
Besides that it helped me to:
* Get to know interesting people outside of my bubble. I've been in CS academics for over 10 years now and it is so refreshing and mind-opening to talk to people of different backgrounds
* Get a boost self esteem. Nowadays I can stay calm and natural when talking to people that are new to me. This wasn't the case before. Especially when talking to people of the gender, I'm attracted to.
Bonus: You get healthy exercise (not a joke: most of us bring 1-2 additional spare shirts to the dance to change during one evening) and improved body control for free.
Here are some popular couple dances without particular order. Of course the list is not complete and a single video will not completely represent each dance and its subgenres.
Samba de Gafieira: https://www.youtube.com/watch?v=H9ia7iGVY-M
Forró: https://www.youtube.com/watch?v=FhMHZsvGHlg
Zouk: https://www.youtube.com/watch?v=o_j8SiLBAoU
Salsa/Bachata: https://www.youtube.com/watch?v=U-JofUEsbD0
Lindy Hop: https://www.youtube.com/watch?v=9GTrNLauLrs
Blues Dance: https://www.youtube.com/watch?v=jpPwmclBxiw