Q. Why did Krishna want Arjuna to fight the Mahabharat war?
Krishna wanted Arjuna to fight the War for two reasons:-
Firstly, to uproot Adharma and establish Dharma:-
At the outset, it is important to mention that Pandavs resort to war only after all their attempts of arriving at a peaceful settlement with the Kauravas failed. Neither Krishna nor Bhagvad Gita advocates violence as many tend to believe. In fact, Pandavas were willing to accept even five villages but the Kauravas refused to concede even an inch of land.
Now, coming back to the question, Krishna declares in Bhagvad Gita that,
“Whenever dharma declines and the purpose of life is forgotten, I manifest myself on earth. I am born in every age to protect the good, to destroy evil, and to reestablish dharma.”
The Kauravas clearly, represent adharma in Mahabharta as they were treacherous, selfish, jealous, evil and full of hatred towards Pandavas while Pandavas represent Dharma as they were always willing to tread the path of righteousness and uphold Dharma. Thus, to establish Dharma, the Kauravas had to be destroyed and the war had to be fought.
Secondly, Krishna wanted Arjuna to fulfill his duty as a Kshatriya (Warrior) as is evident from the following verse,
“Besides, considering your duty as a warrior, you should not waver. Indeed, for a warrior, there is no better engagement than fighting for upholding of righteousness.”
Thus, Krishna struck two birds in one shot by encouraging Arjuna to fight the war as Adharma was destroyed and Arjuna successfully performed his dharma of being a Kshatriya.