"mutually" improve each other. I think (but maybe I'm wrong) that the word "mutual" was in the title because it was about the boys and girls getting together to do activities. Now we call it "mutual" for short.

The criticism is that scouts (which is only for the boys) has taken over what used to be "mutual." Now they do like one combined activity a month.

Scouts could be a separate thing of its own for those who are interested in it, and "mutual" could be a thing for everyone to get together and mutually improve each other.