This is an excellent topic, actually.
2 Corinthians 6:14-15
14Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness?
15What harmony is there between Christ and Belial? What does a believer have in common with an unbeliever?
New International Version 14Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
15And what concord hath Christ with Belial? or what part hath he that believeth with an infidel?
King James Version There is a reason for using the word yoked here. The society of those days were very familiar with agriculture, and until the late 1800s, agriculture depended heavily on beasts of burden. Plows were drawn by a pair of oxen or a pair of donkeys yoked together, which the farmer then drove through his field.
Those Corinthians familiar with the Torah would know the verse Deuteronomy 22:10;
Do not plow with an ox and a donkey yoked together. Not only is this a biblical commandment, it makes a lot of sense. An ox is a powerful, work-bred cow, with a large stature and sturdy body. They are very intelligent, but also very obedient. A donkey, on the other hand, is smaller, and as you likely know, has a reputation for being stubborn. This reputation comes from their enormous sense of self-preservation, far more than that possessed by oxen or horses. A donkey will not trust his master when he can see danger. These things make the commandment of Deuteronomy 22:10 make sense. Plowing with an ox and a donkey yoked together is asking for trouble.
This is the allusion I believe Paul was making as he wrote this letter. Christians have an entirely different view on the world than non-Christians do. We are commanded not to love the things of this world, and not to delight in the pleasures of sin. For a nonbeliever, who cannot see what we see and does not believe in the reality of God, these are foolish ideals that don't hold water. We are the ox, who trusts his master to care for him, and they are the donkey, who trusts noone but himself. When it comes time to plow, if we are yoked to a donkey, an unbeliever, someone will get hurt.
Jesus put it best in Mark 3:25;
If a house is divided against itself, that house cannot stand. I wish to expand on that idea a bit. A house divided against itself cannot stand, it is as the house on the sand. An army divided against itself cannot defeat the enemy, they are too busy fighting each other. A government divided against itself cannot rule, it will overthrow itself. A people divided against each other cannot live in peace, they will kill each other. A marriage divided against itself cannot weather the storm, it will end in bitterness and divorce.
"But Raji," you say, "I love him/her. Surely God will minister to him/her through me, and s/he will become a Christian." That's not the way it works. The modern world tends to believe the old proverb that "blood runs thicker than water." You are expected to be devoted to your family, and above all, be devoted to your spouse. As a Christian, however, your highest priority is to be devoted to the divine master you serve.
Now, if you and your spouse are both Christian, this can work. As you are both devoted to serve the Lord God, your desires fall along the same path. Since you desire the same thing, marital harmony is much easier to achieve.
However, if you are Christian and your spouse is not, you have a conflict of interest. Your highest priority is God. Your spouse likely expects your highest priority to be him/her. They will feel betrayed as, time and again, you follow "this so-called 'God'" that they refuse to believe in. You may want to believe that your faith will shine as a witness to them, but it doesn't work that way.
Your spouse will become bitter that you don't put them first. S/He desires the pleasures of the flesh: money, alcohol to excess, lustful sex as a substitute for pure love, wild parties, etc. You desire the more fulfilling pleasures of the spirit. They will think that God is the reason you turn from them and their wickedness, and they will blame Him for it. Their hearts will be hardened towards Him, and you will accomplish exactly the opposite of what you wanted.
We are not of this world, and we fight against the things that it calls pleasure. THAT is why we cannot date outside our faith.