To adequately understand the issue one has to understand both viewpoints.
Proponents of virginity-saving rely on emotional appeals. They frame it as an issue of loyalty to their future spouse, obedience to God, and because they believe sex for the first time will be more gratifying if you wait until trying it with someone you love. None of these are based on the tenets of logical reasoning.
Firstly, one cannot be loyal to a person they have no knowledge of. To be loyal to someone means that you act in accordance with their wishes. If you have no knowledge of someone then you have no knowledge of what their wishes are. Your future wife might wish for you to be an experienced and skilled lover. How many things have you done skillfully on your first try? How many skills have you honed sharply with only one perspective from which to critique? You might say that you only need one perspective from which to hone your skill if that is the only perspective you are trying to satisfy. This is false because that perspective, your spouse, does not know what he or she does not know. How many people have lived their lives never searching for the G-spot because they didn't know it was there? How many men and women never said to their partners "play with my anus while you fuck me" because it never occurred to them that it magnifies the sensation happening in their other genitals, and no one ever told them? How many people have never experimentation with sensory deprivation, role playing or asphyxiation? We are only the sum of our experiences and nothing more.
Second, the Bible was written by men and is not the word of God. However, the Bible is very real as a written document and it is surrounded by a context. To understand why the Bible's authors want you to save your virginity is to understand why the authors thought it worth writing. At the time the Bible was written there was no technology for contraception, and there was no reasonably safe or reliable way to abort pregnancies; therefore, having sex = making babies, every time, no matter what. It was and is in the interest of society not to have single mothers raising hoards of children on their own. It would be much better if every woman with children also had a man to share the burdens of raising children and contributing to society. If religion is seen as a tool of social control, which is exactly what it was and is, then suddenly many of God's directives and commandments make perfect sense because they just happen to be necessary for society to exist peacefully and thrive in those ancient times. The authors obviously wanted to enforce solid family units because it was to benefit society. As time changes so does the human social matrix; unfortunately, the Bible has not changed. Interpretation of the Bible changes, but there is only so much you can do to change the meaning of things otherwise stated plainly. In this particular issue, sex no longer means having children. Contraception makes the liklihood of child-making relatively low and abortion takes care of those times when contraception fails. Suddenly, two uncommitted people having sex does not lead to the destruction of society, as it would have before contraception and safe, reliable abortions. This particular tenet set forth by the bible is now out of date and no longer necessary.
Lastly, Sex for the first time is almost never gratifying for either party. It may be an overall pleasant experience, it may have a positive emotional impact, but anyone who says their first time having sex was their best sexual experience ever is either a liar, or has only had sex once. Speaking only for myself, I didn't have sex until well into adult hood and it was with someone I loved deeply. The experience was awful and she was dried out and remained unfulfilled before I stopped, unfulfilled myself. I later learned to become a very good lover indicating that my first experience is not a representation of what would be a trend for me. It's just that doing something, anything, for the first time typically is done unskillfully.
There are some good reasons not to wait for marriage.
First, sex is fun, healthy and it feels good. Both parties are engaging in a physical activity, receiving validation of their attractive worth, and getting an orgasm.
Second, becoming a good lover is something learned with experience. No amount of studying on the internet or porn-watching will prepare a person for being a sex god in bed, master of multiple body shaking orgasms. I for one plan to rock my partner's world from the first time until the day one of us dies.
Third, you are not guaranteed a wife or a future. People die and that is a fact. leaving things off until tomorrow means you take the risk of depriving yourself of that thing forever. Your only get one chance to live before you die and once you die that's it. What happens after death? Easy: it's the same thing that happens before you were formed in a test tube. Do you recall what it felt like before being born? There you go.
Last, marriage is not for everyone. Some people do not want to be married. Maybe they have attachment issues, maybe they hate the opposite sex, maybe they are not religious (marriage is a religious ritual...) or maybe they know they would be unsuitable as a spouse.
I would like to conclude by suggesting that there is only one good reason to hold off on sex (not the same as waiting for marriage): there is no way to guarantee that sex will not result in a baby other than removing or severing sexual organs completely, which is permanent and not reversible. From a female perspective, this is not a problem if you are OK with abortion and have the funds to foot the bill. From a male's perspective this makes sex a risky proposition. The decision to abort or not is not yours to make, and even if your partner claims they would abort a fetus there is no assurance they won't change their mind. You risk being legally obligation to provide financial assistance for a child for 18 years, in America. Therefore, for males, the only safe time to have sex is when you want a baby with your partner. At all other times it's a risk. This applies to married people as well. Being married =/= ready to have babies.