We are not given a specific reason in scripture as to why the Apostle Paul did not marry. So we can only make presumptions based on Jesus’ advice and the advice Paul gave in his epistles.
In order to fulfill one’s consecration vow to the Lord, the Apostle Paul states that the unmarried have a position of advantage. Why? Because when people are married, our minds and actions naturally focus on pleasing our spouses. Whereas when a person remains single, he may focus more of his attention on serving and pleasing the Lord. (Please read 1 Corinthians 7:25-40.)
Yet the Apostle Paul’s advice to remain unmarried is not a command. 1Corinthians 7:35,36, “I am saying this for your own good, not to restrict you, but that you may live in…undivided devotion to the Lord.” Please recognize Paul is not teaching that Christians are forbidden to marry. The restriction to remain a virgin is a false teaching. Timothy addressed this error in 1 Timothy 4:1-3, “…some will abandon the faith and follow deceiving spirits and things taught by demons…they forbid people to marry…” Marriage is still honorable when the relationship is sustained in purity and holiness, as God designed. Hebrews 13:4, “Marriage should be honored by all, and the marriage bed kept pure…”
Marriage can be a distraction from our consecrated walk: 1Corinthians 7:33, “But he who is married cares about the things of the world – how he may please his wife.” Jesus explained that our focus in life should be doing God’s will and that we must be willing to give up everything, even our family, in order to achieve the prize: Matthew 19:29, “And every one that hath forsaken houses, or brethren, or sisters, or father, or mother, or wife, or children, or lands, for my name’s sake, shall receive an hundredfold, and shall inherit everlasting life.”
Paul's choice not to marry was likely because He was so devoted to following Christ, and so devoted to making his calling and election sure, that he did not permit any distraction to keep him from his goal. Even though taking a wife is an honorable act, it is a fleshly, natural act. No doubt Paul had Jesus' words on his mind continually: Matthew 6:33, “But seek ye first the kingdom of God and His righteousness, and all these things shall be added to you.”