According to the speaker of "The Sonnet-Ballad" by Gwendolyn Brooks, why do people fight wars? Is it because they are forced to fight, see war as beautiful, believe in their religions, or want to protect their country?

I think the question is written in multiple choice format, and the four choices are given. To answer your question based on the four choices present, people fight wars because of the second option. They see war as beautiful.
The poem's narrator is a woman grieving the loss of her husband. She has lost him to war, and the poem personifies war as a beautiful and seductive lover that lures men away with its arms. Line 8 of the poem is where the loving relationship between men and war begins to take shape.

That my sweet love would have to be untrue.

The speaker tells her readers that her lover/husband is going to be untrue to her during this war. It causes readers to think that perhaps the man is being untrue with another woman in some far off city, but that isn't the case. Lines 9-12 really drive home that the man's love is being seduced away from his wife by the beauty of war. Its "arms" pull him in, and he is smitten with its "coquettish death." The thrill of battle and near death experiences are essentially war's way of flirting with men and appearing gloriously sexy.

Would have to courtCoquettish death, whose impudent and strangePossessive arms and beauty (of a sort)Can make a hard man hesitate––and change.