Unfortunately, this and parallel passages have been wrongly used all too often to justify the abandonment of responsibilities to family in the name of following Christ.
But Christ is not here advocating repudiation of family. Instead, He insists that our allegiance be to Him and to His will. Nothing must be allowed to usurp His rightful position of supremacy in our lives. While it is true that for some a life unencumbered by family duties may result in more efficient ministry (1 Corinthians 7:1-9, 25-38), family relationships and responsibilities are of great importance to Him (vv. 10-24; see also many other passages).
Consider the case of Elisha. God had instructed Elijah to train Elisha to take his place as prophet (1 Kings 19:16). Finding Elisha plowing in his father’s field (i.e., family duties) with 12 yoke of oxen, "Elijah passed by him, and cast his mantle upon him" (v. 19).
Elisha knew immediately that he was facing a dramatic change in his life. He did not refuse, argue with, or try to alter the call, but he did recognize a responsibility to his parents. "Let me, I pray thee, kiss my father and my mother, and then I will follow thee" (v. 20). Elijah agreed. To solidify his determination to leave, Elisha immediately sacrificed a pair of oxen, using as fuel the plowing instruments he had been using. He was, in effect, making a clean break with his former life, yet honoring and respecting his parents.
"Then he arose, and went after Elijah, and ministered unto him" (v. 21). JDM