Why did the Japanese fight so hard at iwo Jima?

1. Iwo Jima was the beginning of actual Japanese terrritory. 2. The mission of the defenders on Iwo Jima, was to buy time with their lives, so that the Homeland (Fatherland/Motherland) would have more time to prepare their defences. 3. If the US/Allied casualties were high enough, reconsideration on the part of the US/Allies might alter any invasion plans for the Homeland. (Which did occur during the Okinawa invasion, which came after Iwo Jima).