Thank you for the question on marriage, “Where in the Bible does it say marriage is not for everyone?”
There are two Bible passages that addresses marriage and it’s exceptions for one’s consideration.
A. Jesus said this in Matthew 19, “7 “Why then,” they asked, “did Moses command that a man give his wife a certificate of divorce and send her away?” 8 Jesus replied, “Moses permitted you to divorce your wives because your hearts were hard. But it was not this way from the beginning. 9 I tell you that anyone who divorces his wife, except for sexual immorality, and marries another woman commits adultery.”
10 The disciples said to him, “If this is the situation between a husband and wife, it is better not to marry.” 11 Jesus replied, “Not everyone can accept this word, but only those to whom it has been given. 12 For there are eunuchs who were born that way, and there are eunuchs who have been made eunuchs by others—and there are those who choose to live like eunuchs for the sake of the kingdom of heaven. The one who can accept this should accept it” (A searchable online Bible in over 150 versions and 50 languages). Citations are from the New International Version.
Jesus gives three reasons why a person may not marry in verse 12. There are people who are born that way. There are those who are castrated and have no desire to marry. Lastly, there are those who choose to remain single for the sake of the kingdom of heaven.
B. The Apostle Paul affirms Jesus’ teaching on marriage and celibacy
II Corinthians 9 says this, “3 This is my defense to those who sit in judgment on me. 4 Don’t we have the right to food and drink? 5 Don’t we have the right to take a believing wife along with us, as do the other apostles and the Lord’s brothers and Cephas? (NIV). It appears that the Apostle Paul did not exercise his right to marry a believing spouse even as the Lord’s brother and Peter had a spouse.
I Corinthians 7 says this, “Now for the matters you wrote about: “It is good for a man not to have sexual relations with a woman.” 2 But since sexual immorality is occurring, each man should have sexual relations with his own wife, and each woman with her own husband. 3 The husband should fulfill his marital duty to his wife, and likewise the wife to her husband. 4 The wife does not have authority over her own body but yields it to her husband. In the same way, the husband does not have authority over his own body but yields it to his wife. 5 Do not deprive each other except perhaps by mutual consent and for a time, so that you may devote yourselves to prayer. Then come together again so that Satan will not tempt you because of your lack of self-control. 6 I say this as a concession, not as a command. 7 I wish that all of you were as I am. But each of you has your own gift from God; one has this gift, another has that. 8 Now to the unmarried and the widows I say: It is good for them to stay unmarried, as I do. 9 But if they cannot control themselves, they should marry, for it is better to marry than to burn with passion” (NIV). A person may have such control over his/her passions that s/he may choose not to marry for the kingdom of God or for personal reasons.
SUMMARY: Marriage is not necessarily for everyone for one has to be less self-centered and more other-centered if that relationship is to be more harmonious.
For more perspectives:
https://www.quora.com/Where-in-the-Bible-does-it-say-marriage-is-not-for-everyone