why does it prefer T state if it wants to hold breath for a longer

I was wonderingFor hemoglobin for crocodiles why does it prefer T state if it wants to hold breath for a longer period of time? I thought it would want to prefer R state if it wants to hold onto the oxygen. and furthermore how is T state harder to bind O2 but also harder to release O2? I thought T state is easier to release O2. I thought R state was closer to Myoglobin curve not T state.