Why was the battle of Thermopolae fought?

Answer 1

The Greeks had determined that, due to the threat of the Persian fleet and its amphibious capacity to attack and defeat the independent cities one by one, and as it also protected the Persian sea supply lines, that they had to defeat that fleet. As it was superior in size and numbers, they had to catch it in narrow waters to neutralise its superiority, so they set up a small blocking force in the narrow pass at Thermopylai to hold up the Persian army plus its accompanying fleet in the narrow strait nearby, and force a naval engagement to turn the position.

The blocking force had to hold on long enough for the Greek fleet to defeat the Persian fleet. After three days of naval engagements, the Greek fleet came off worst and withdrew to Salamis near Athens. The land force dispersed to the cities and the rearguard protecting the withdrawal was anihilated.