The Horde needs the alliance and the alliance needs the horde. They make eachother strong and help to remind eachother what they as a faction stand for. Garrosh loves his horde but totally ignores the fact that the horde he loves would not even exist if not for the alliance. Only the wise horde leaders like Lor'themar, Vol'jin and Saurfang understand this.
Now more OT: Love him as a leader, he's probably the most intelligent and tactical leader the horde has. Would he make a good warchief though? Probably but it won't happen due to him being to human looking and being needed to watch over Eastern Kingdoms. Obviously can't rely on Slyvannas for that(or anything really). He just doesn't fit the role. Saurfang will get the role, as he fits all the qualifications and currently has no other major responsibilities.