Why was the Battle of Thermopylae fought there

The Greek defensive strategy to defeat the Persian invasion was to first defeat the Persian war fleet which so threatened the Greek city-states with amphibious attacke that they kept their armies at home to defend their city. This enabled the Persians army to pick off each city in succession rather than face the full force of a combined army.

So the Greek stated decided to first destroy the Persian fleet to both remove the threat and allow their forces to join up to oppose the Persian land force, and to remove the fleet protection of the shipping supply line which sustained the Persian army from Asia Minor.

To force a sea battle in constricted waters which neutralised the numerical and size superiority of the Persian fleet, they held the pass at Thermopylai to force the Persians to break the impass by a sea battle in the nearby strait in order to outflank the position. The pass held for three days, while naval engagements went on in the strait. Unfortunately for the Greeks, they got the worst of it and withdrew their fleet.

With no reason to hold the pass, the city army contingents were sent off home. To delay the Persiancavalry from riding them down in oven country, the Spartan contingent continued to hold on to let them get away and was anihilated.