Sango losing his emotions had taken a great toll on his mind, leaving behind only his rationality and making him no less than a robot.
Hate, guilt, love, betrayal, affection. And every of such emotions that completes one and differentiate them from an empty tusk, those are what Sango lacks.
Getha losing her tribesmen and her father, mother at the same time must have brought her pain and agony.
That is what Sango thought of her situation when he heard about it.
It never occurred to him just how intense the agony she was feeling is like or in what way the agony really affected her.
None of those things ever occurred to Sango, and he never once took it upon himself to try to understand it.
When he discovered that he was betrayed by his own fiancee, the first thought that occurred in Sango's mind was to logically analysis the reasons for her betrayal.