Why are some of the Groups members belong to not showing up on their profiles?

[Susan E.]

If a member has checked the “Do not show this Group on my "View Profile" page” option for a given Group, his/her membership in that Group does not show up on his/her profile.

Another reason a Group may not be listed in members' profiles is that the Group has been created as a private group, with the setting "only participants can find group". That setting essentially makes the existence of the Group "invisible" to non-participants - which means the Group is not displayed on a person's profile page.