DISCLAIMER: This is a mature topic only intended for people who've at least begun puberty. If you are less than 13 years old then I pray you don't have any reason to concern yourself with this yet, and you should ask a trustworthy adult before reading this.
The first two words God ever said to us (humanity) are recorded in Genesis 1:28. He said "be fruitful." While this should make a lot of people happy, there are certain ways to go about this that are proven to work well, and other ways that... well... not so much. Be it an axiom or maxim, living together is synonymous with having sex without first marrying (which can technically be called fornication). A person who's never had sex is a virgin. Here are the direct references where God, in His word, warns us of His expectations of our purity.
Notice in the original law1 that as soon as a man had sex with a woman he was commanded to marry her. This is not to say that "two wrongs make a right" (note that sex is a benefit of marriage, not the other way around) but to minimize the effects of the sin.2 Also notice that even if the girl's father thought the boy was a loser, and didn't let them marry, the boy still had to pay a fine.3 Both of these details were obviously intended to drive home the point of how significant sexual relations are, and specifically how it's only meant to be in a context of marriage.
If you want to point out the technicality that forced rape is way different than consensual cohabitation, then keep in mind this was written a few thousand years ago. In the culture this was written, no self respecting woman would be caught dead having sex before marriage (Judges 11:36-40, 2 Samuel 13:11-13). Because the men in that culture were very particular about marrying virgins (Leviticus 21:13, Deuteronomy 22:13-19, Judges 21:11-12) so sex before marriage meant condemnation for life that the only man who'd ever want her again would be a man seeking a prostitute (Leviticus 19:29). Cohabitation requires two consenting parties, so there was no need to specifically condemn the activity, it was adequate to just condemn rape. It wasn't until the New Testament and Christianity spread to the gentiles (non-Jews) that scripture needed to address consenting parties (fornication).
Living together is essentially pretending to be married (taking the benefits of marriage without the responsibility & commitment) and implicitly says "I don't trust you enough to marry you first." This is a mixed signal because the fact that they're having sex implies a level of intimacy that is reserved for marriage (Exodus 21:10, 1 Corinthians 7:3). We aren't supposed to do that to another human being: we aren't supposed to tell them we love4 them in order to get in bed with them (1 Corinthians 13:4-8). This would be living a lie, or as Revelation 22:15 puts it, living in "falsehood," and giving in to lust, rather than honoring our Creator. For those who reply that their parents divorced and their partner's parents divorced and all their friends divorced and divorce is expensive, etc., then consider my spinoff, Family in the Bible, here.
Saying "marriage bed" here is as clear as it gets without using the graphic phrase "don't have sex outside of marriage." It's not an attempt to be cryptic, vague, or spiritual. Compare to when we get sick. If we worked in the same company, on the same team, and we were in a meeting together, and I'm calling in to the meeting from home because I'm sick and possibly contagious, and you ask how I'm feeling. I could tell everyone on the phone "I have diarrhea," or I could say "I'm on the B.R.A.T. diet." the later is so much more gentle, polite, and less graphic of an answer, but they both mean exactly the same thing. That's what the author of Hebrews was doing here.
In the modern western world marriages are initiated by love but in the grand scheme they are (should be) more about commitment than they are about love. Sex before marriage undermines the absolute commitment of marriage (instills the "try it before you buy it" mentality) which irrevocably taints the presence of unconditional love which was intended to be fully present.
It is a bad example for your inevitable children and/​or all other children (people) in your lives.
It encourages child conception outside of an absolutely committed marriage and allows for the parents to easily separate thereby (a) destroying the family unit that God designed5 and (b) damaging the parent/​child relationship that is intended to model the God/​human relationship. These problems give children a desire to say "if God could not keep my parents together then he cannot do anything for me either".
It is especially a bad witness to non believers if believers do this because it allows a non believer the opportunity to say "your morality is no better than mine so your God must be no better than mine" (Romans 2:24).
At its highest level and at its core, this idea is dangerously close to a belief (whether active or passive) that "yeah, God may have said marriage first is the best way, but I am willing to bet my life (and yours) that I can do it better, or at least different, and still end up just as good." (Ezekiel 36:23)
If we want to talk about economic exceptions, then granted maybe there are a few examples where it may be temporarily justifiable to live together. But most people use this as an excuse rather than a last resort. We should also be clear this exception only applies to so few people they could be measured in PPM (people per million) not percent of the population. And sex by any definition should never be entertained outside of marriage. (This includes one night stands, date nights, fornication, fooling around, etc.) Finally, I sincerely hope all marriages last a lifetime, no matter how they start off, because that is the way God created it (Matthew 19:4-6, Mark 10:6-9). But regardless of what we want to believe, this practice is no less dangerous than playing with fire (Proverbs 6:27).
Here's a great quote from Erwin McManus, pastor of a couple thousand twenty- and thirty-somethings in Los Angeles. This was part of his 2007 sermon series titled 'Romance Unwrapped':
"The way you can circumvent the process is you can start having sex. Because having sex gives you the false perception that you've now moved to intimacy. It gives the woman a sense of intimacy and it give the guy a way out of intimacy. But... once you start having sex before marriage the level of intimacy, true intimacy that you have, is pretty much as far as you're going to go no matter how long you're together and even if you marry. Because you basically have stunted the relationship at that level of intimacy. And so what's going on here is that a lot of you are pretending to move toward real relationship by having sex. And when people ask me who could you marry, I tell them marry the person you can talk to all night without ever needing to have sex to have intimacy."
Arguably the trick here is more verse 2 than verse 1, but God knows the reason verse 2 happened was because of verse 1. This happened to the poor old Israelites, same thing happened to rich man Solomon (1 Kings 11:1-6), to King Ahab (1 Kings 16:29-33), and it can still happen to us today. That's why God warned us many times, including Exodus 34:15-16 and Deuteronomy 6:10-15. There wasn't an explicit "command" to quote from this story, but we can see (a) God ordered some executions and (b) when an execution was done it was rewarded. This doesn't mean we should execute people on our own volition, but this principle again reminds us of the significance of sex and how we shouldn't take it lightly (as our culture has decided to). It's not like He's being the neighborhood bully when He says this. God provides us everything (Acts 17:24-31, Revelation 4:11), He just wants the credit He deserves, and He gets ticked when we give that credit to anything else (Isaiah 42:8).
2 Samuel 13:1-22
At first this story may seem really weird. I remember wondering why Amnon hated Tamar after getting what he wanted. But my conclusion is he used sex to gratify his fantasies, and he found out the hard way that real life can never live up. As great as sex is, if we fantasize about it then it can't possibly live up to our expectations, because God gave us very creative imaginations. And this is about more than gratifying our fantasies. It's also about pleasing the other person, and in Ammon's case he found out it's just not fulfilling when it's used as a personal gratification rather than an expression of fully committed, bidirectional, exclusive, love. And remember, the primary purpose of sex is to make it fun to start a family so that we can fulfill God's command in Genesis 1:28, and then to be a reward for maintaining that family as the prophet reminded us in Malachi 2:15. Even in marriage, it's dangerous to expect sex to truly fulfill our fantasies. Also, just because super models are (generally speaking) strikingly more attractive than (for example) cafeteria workers, that doesn't mean that sex with a model will be better than another person. It just doesn't work that way6. At best it would be marginally better. This is supposed to be a good thing, so that we can all enjoy it, not just the genetically gifted, but that ruins our fantasies. So be warned about the expectations you put on this one singular activity. Guys, don't think that dumping this girlfriend (who's reasonably attractive) for that girl (who's more attractive) will necessarily result in more happiness. Look more than skin deep or suffer the disappointments (1 Samuel 16:7).