2 Corinthians said:
6:14 "Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness?"
6:17 "Therefore come out from them and be separate, says the Lord."
7:1 "... let us purify ourselves from everything that contaminates body and spirit..."
This parable looks at the old way of transportation. You'd have a cart pulled by a pair of oxen or pair of donkeys. If you have 1 oxen and 1 donkey, they won't pull the cart very well, if at all. One of them will drag down the other.
Compare this to an atheist dating a Christian. The Christian might be firm in his morals and be biblically convicted to hold them. But after dating someone for awhile, specifically someone who doesn't care much for boundaries, you grow to love the person, and your religious convictions can have a tendency to melt away. You may find yourself trying to justify your actions, as that is what Satan will want you to do. Sin has a way of knocking at your door when your guard is down.
God said:
Extra verses:
1 Thessalonians 5:22 "Avoid every kind of evil"
1 Corinthians 6:18 "FLEE from sexual immorality..." -- literally get up and run away as fast as you can, screaming and hollering at the top of your lungs.
Paul does not say we should isolate ourselves from non-believers. Rather, Paul wants believers to be active in their witness for Christ to nonbelievers, but they should not lock themselves in personal relationships that could cause them to compromise their faith.
Believers should do everything in their power to avoid situations that could force them to divide their loyalties. This is especially true in relationships where (in our society) sexual sin is displayed as normal and even encouraged by many people.
Now, Romans 14: 13-23 says simply, "Do not do anything if it might cause your brother to sin." If I am dating a non-christian who is an upstanding citizen and VERY moral, your friend might say, "If it's okay for him to date a non-christian, then I will do." You friend could end up with a crazy heathen and follow the path to sin. The bible says that YOU are guilty. That punishment is worse than if it had been yourself.
From my personal experience, you HAVE to set boundaries IMMEDIATELY in a relationship. My girlfriend and I have been dating for nearly 4 years, and we make sure we don't pass that thin line that society and Satan tries to convince us isn't real. We have not and we will not put ourselves in that situation.