Why is Billie Jo's father important to her in "Out of the Dust"?
The most obvious reason Billie Jo's father is important to her is because he is all she has. When her hands are burned, Billie Jo loses her only immediate hope of escaping their dying farm. Her mother and baby brother are dead, her friend Livie gone West, and Mad Dog, her only potential suitor, has escaped the barren Oklahoma Panhandle through his musical talent. Billie Jo's father is the only one left with her.
On a deeper level, however, Billie Jo knows that she is "(her) father's daughter", and essentially, to deny him would be to deny herself (January 1935). The situation is similar to what Billie Jo learned about home, by running away from it on the westbound train -
"I went looking for something, but I didn't see anything wonderful. I didn't see anything better than what I already had" (November 1935).
The lesson Billie Jo learns about the land holds true for her relationship with her father as well. She realizes,
"I can't get out of something that's inside me" (August 1935).
Despite his many faults and inability to communicate, Billie Jo's father loves her. He shows it in his actions, as when he searches for her all night when she is caught in the dust storm (March 1935). His love for her is constant, and he
"stay(s) rooted, even with (her) tests and (her) temper, even with the double sorrow of his grief and (her) own, he had kept a home" (August 1935).