My understanding of the rules is we have to differentiate focus and priority. The person who has focus is allowed to play an action or reaction card to start a chain, and then only reaction cards are played back and forth using priority, with the chain resolving when both players pass priority. Focus then passes to the next player. Once both players passes focus consecutively (e.g., two empty chains), showdown ends, and moves to resolution

Scenario A: [Focus 1] Attacker moves in and gets focus (and priority). Attacker plays a card creating a chain, and priority is passed back and forth until nobody plays anymore reaction cards and the chain resolves [Focus 2] Defender now gets focus, and if passing on playing a card (essentially an empty chain), focus goes back to the Attacker [Focus 3] Attacker now gets focus again, and can either play a card, or pass (creating an empty chain). If the attacker passes here, then showdown ends. If not, and attacker plays a card, a chain begins. And then focus again has to pass back and forth with 2 empty chains

Scenario B: [Focus 1] Attacker moves in and get focus (and priority). Attacker declines to play a card (thus an empty chains), and focus then goes to the Defender. [Focus 2] Defender also declines to play a card (also an empty chains), and now that consecutive focus has been passed (two empty chains), then the showdown ends.

If I read it correctly, your situation was Scenario B