AT&T is already in the high speed Internet space.
The complaint is that if they gain ownership of HBO, Warner Brothers (movies/TV), and the Turner channels then they can then hold other TV competitors to ransom by demanding higher channel fees that get passed on to consumers. Also (in the complaint) that they could make it more difficult for TV-over-internet services like Sling to compete in future.
The antitrust complaint actually has some merit, since allowing content companies to merge with traditional TV/cable providers just at the point that cord-cutting alternatives are becoming more common (thereby kneecapping the cord-cutting companies) seems like a bad bet for consumers.