Losing love towards one another eliminates the critical characteristic of Eternal Life, and prevents guidance by the Holy Ghost. Other motivations for action take precedence, and righteousness is not part of the equation.
Hate and anger, which become so prevalent in times of war, can take over the hearts of both sides. Hatred and anger are even used as a viable strategy for winning. According to our brother here in the Edgemont Stake, Dr. Demetrius Kepas (who was a teenager in Athens), intense hate and anger permeated the Greek Civil War with the communists; as he personally reported in class, he observed that hate, and how anger took over.
In a much earlier example, the Iliad is the great epic of the Greek war against Troy. The whole story is about Achilles throwing temper tantrums. For years, he was so angry and obsessed with the anger, that he drove out all feeling of love and concern, even for his dearest friend, Patroclus, who eventually was killed.