The family farm was entrusted to him, and his relatives were buried out back.
He was being stubborn, and frankly had little reason (from his perspective) to believe that moving would do any good: why would he trust NASA to heal his son, when NASA had stolen his father?
And why would he even care that much? Earth was dying and so was everybody on it; frankly, he may even (on some level) have felt jealous of his kid, who theoretically wouldn't live long enough to have to suffer through the extinction of the human race. Just what would be the point in having him cured, really?
Not to mention Tom appeared to be rather unhinged, so it's not as if he was making rational decisions.