aside from the HE thing, your post could have been about me as a child.
I hated with a passion any organised clubs / classes. I was taken to them all, to see if I got on with any of them, and just did not enjoy it. I once came back from Sunday School and said I wasn;t going back as all the kids just ran around like headless chickens 
I preffered one to one, reading, less sociable activites. I also hated kids club type stuff on holidays too.
If you want them to take up a sport for their own personal development, what about something less sociable, such as swimming or rock climbing?
On the whole, I am now very rounded and able to socialise with most people, DH loves taking me to work 'dos' as I will happily natter to anyone about anything. I still like my own space, though, and will sometimes need an hour to just relax away from everyone.
Im sure your daughters are wonderful and perfectly happy. Don't push them to try and fit them into a mould they just wont fit in, but let them know thery can ask if they want to do certain actitivies etc.
I found the best 'social' activity when I was young was sleepovers. I used to have one every few months and have around 10 friends to sleep. Im not sure why I enjoyed these but not other events, just did.
Hope this has put your mind at rest in some little way, and you seem like a lovely mum to not force them into stuff they clearly arent happy with.