These relatives are awkward to introduce because they're not necessarily your friends, but technically not your relatives either. You don't want to insult him by going into detail about his relationship with your sister in public, but if you call him your brother-in-law, awkwardness might arise when people glance at the non-existent wedding ring.
This also applies to would-be parents and sisters-in-law.
Ted: Are you kidding? Then my father-in-theory's gonna want to join too. There's a reason I didn't marry into that crazy family, ya know.