Quick recap of Tom's life in Interstellar: everyone he loves dies. He loses his mother, his father, his first son and his grandfather. After his dad spends Tom's childhood making it clear he prefers Murph, he then abandons the family and leaves Tom his worthless farm and truck. After a life of pain, Murph berates Tom for being stuck in his old-fashioned ways even though that's all he knows because he wasn't allowed to pursue higher education.
But why does Tom not want to leave even if his son is dying?