Why didn't Balram (brother of Krishna) participate in the Mahabharata War?

Both Duryodhana and Arjuna approaches Krishna for his support. Krishna offered his entire army to one and himself to other with a condition that he will not take up arms during the war. While Duryodhana triumphantly accepted the army, Arjuna chose the non fighting Krishna.

Besides, as an avatar of Sheshnaag, on whom Lord Vishnu rests, Balram could not have fought against Krishna. So he decided to go on a pilgrimage while the war carries on.

Balram was neutral. He did not take part in the war, as he could not make sense of the carnage.

Balarama too favoured Duryodhan because he pleased him as a disciple but did not think further about consequences. Krishna foil every plan of Balarama to form alliances with Duryodhan, because neutrality is not an option to cause radical change.

Finally when Bhima killed Duryodhan unfairly, Balarama was so furious that he raised his plough to kill Bhima. Krishna pacified him by saying that, “Oh, now you are here to establish dharma? When you were needed, you went on a pilgrimage. Why did you come back now? When Draupadi was pulled into the court by her hair, you did not get angry. When they tried to disrobe her, you did not get angry. When the Pandavas were sent to the forest after being cheated in the game, you did not get angry. And when they completed their full term of exile like fools – anyone else would have come back and attacked – after thirteen years, they were not given what was due to them, but you did not get angry. Now your favorite disciple is lying here with his manhood shattered, you are angry and you want to protect the dharma. Leave this place! Protecting the dharma is not your business, because you have never participated in that.