Why British carrier aircraft lagged in 1939

Did the Fleet Air Arm assume carrier aircraft could never match land-based performance?

No. The Navy had planned higher-powered aircraft, but the war began before their engines were ready and the RAF then received priority.

The Royal Navy ordered 2,000-horsepower engines after regaining control of the Fleet Air Arm. Had war begun in 1942 instead of 1939, those engines might have supported carrier aircraft comparable with contemporary American and Japanese types. The conflict began before the powerplants and aircraft were ready. When the engines became available during the Battle of Britain, the RAF had first call on them. Timing and industrial allocation mattered as much as naval design ambition.