Adversarial DMing? When the DM sees his role as being an adversary of the players.
I have a tale of what I consider to be the epitome of it.
A DM had planned an adventure for his table. It was a raid on a stronghold. He, with the help of a friend, planned who was on guard at what shift, and how forces were distributed.
After the game I asked him about it. He described the conflict, their battle with the court high wizard in the middle of the night, backed by his top aide.
I was curious: Why did they end up facing both? Was't one supposed to on duty at night, and the other during the day?
His answer? "I had to make the defenders stronger. The party was winning."
He took it personally if the party won a battle that he didn't plan on them winning. He argued that it was his job to "present them with a challenge.". What that meant though was that he'd raise the bar as things progressed, so that no matter how well they planned, no matter how well they coordinated their actions, it was always a coin toss, at best.
End result? The players in his game gave up anything resembling planning, cooperation or teamwork. The best you could do was earn the DM's wrath the next game when he next ran.
After a big victory, half the players would make it a point to miss the next game session, so they wouldn't be there when the DM "got even".
I don't play at that game any more.
In my own view, the DM has to "wear two hats", with regards to the game.
First hat, worn when planning the game session/adventure: Playing the part of whatever Big Bad is involved, he/she has to plan for the defense of whatever it is the PCs are going after. This should be done within the limited resources said Big Bad has. No new or additional resources should be invented for this part, but it should be done with full malice. The PCs are the enemy.
Second hat, worn during play: The DM should be the impartial arbiter of the game, implementing the Big Bad's plan as written, but without favoritism. The DM isn't god, because in these games the gods play favorites. He/she has to be better than that.
The DM I mentioned would insist that he be present when the players made their plans. He needed that so the bad guys could be prepared. On one occasion the table split into two groups, each walking to a separate room. Both groups made battle plans, and whichever group the DM listened in on was the plan that would be discarded.
The DM accused the players of cheating.
Like I said, I don't play at that table any more. By the way, the DM was and is a good friend. He's just not someone I care to play with any more.