4. “All anger is reasonable” is false?
I agree. Everyone who feels angry has at that moment a "reasonable" reason for feeling angry. We can come up with some justification for responding with anger.
This justification, though, can be based on false conclusions. I may see a threat where there really is none or think there is a loss that has not really occurred.
I remember becoming very angry with my seven-year-old son after being hit by a rubber band while I was watching tv. My first reaction was based on the belief that he purposefully shot the rubber band at me. After reacting in anger, I realized I was wrong, that the incident was entirely accidental as he sat playing with the rubber band.
At the moment I reacted, I believed my anger to be entirely justified. It felt reasonable to me. Then I discovered I was wrong. The anger left me, replaced by guilt in acting too hastily.