Facebook – Message Upon Leaving a Group

Facebook does not provide a way to have groups that anyone can join instantly. Someone already in the group must add them, or they can request approval from a group admin.

The likely reason for not providing this is that it would attract spammers. Old-style open groups had spam problems and they did not even have the new group notification or chat options. Unlike posting to a page, all group members are now notified by default of any new post to a group, and also for groups with no more than 250 members it is possible to send chat messages to all members of the group including people who are not confirmed friends.

If you want anyone to be able to join and don't care about the notification or group chat features, then you may want to use a page rather than a group.

From Facebook's point of view, this is a feature, not a bug. FB wants group admins to deal with members ASAP. Your main options are:

(edit: open groups have the same approval issues as closed ones)

1. change it to a page so people can join without approval.
2. change it to a secret group so people can't request to join.
3. give up your admin role and have someone else deal with it.

See also: Any way to auto-approve requests to join new-style Facebook group?