Why the common-mode gain of the differential pair is almost zero?
If Vin1 and Vin2 rise together (within reasonable boundaries of the upper and lower power supplies), Vout and Vout2 don't change at all.

You have a current source and that is contant and the current is spread equally between M1 and M2. It's still spread equally between M1 and M2 when Vin1 and Vin2 change together. The current through M1 and hence through R1 remains the same and therefore Vout1 remains fixed.

So when you say a text book says Vout1 and Vout2 both rise this text book is incorrect.