The Atlanta Falcons square off against yet another opponent outside of their current division that has had their number historically. This actually describes the majority of the NFL.
The Dallas Cowboys, so successful up through the 1990s, used to make it a habit of beating up on the Falcons. They lead the all time series 19-11 and it was an ugly start for Atlanta.
Through 1985, Dallas won eight of the first nine matchups against the Birds, including Atlanta’s first two ever playoff defeats — one in the 1978 season and one in the 1980 campaign.