https://xkcd.com/592/ [comic added later]
In this time and place, the secular world does not place a high value on chastity, which seems to be regarded as some sort of eccentric religious virtue. So long as one avoids disease, and harassment in the workplace, and uses contraception to avoid "unwanted pregnancy", the only touchstone is consent. (Since paedophilia is still taboo, "consent" is interpreted using a legal fiction that says that those below e.g. 18 cannot consent.) Married types are often faithful to their spouses, but the unmarried do what they like.
It is true that there are some distinctively religious (as well as some distinctively Christian) reasons to be chaste. But it is silly to think these are the only reasons. Traditional sexual morality is not founded exclusively on mystical doctrines about God. It is also based on practical experience, concerning some basic biological and psychological facts about human beings. Facts which are going to operate regardless of your opinion about any transcendental realities. That is why most traditional cultures have discouraged fornication, even those which have quite different doctrines about the gods and the meaning of earthly pleasures. It is not because they listened to their priests, but because they listened to their grandmothers.
I will however have to assume one mystical dogma in this post, namely that there is such a thing as ethics, which commands do not harm your fellow human being, and that this rule is obligatory. Furthermore, that one's fellow human beings includes ONESELF, so that the ethical person is first and foremost committed to human flourishing in the one example of humanity which they actually have control over. Therefore, you cannot excuse a self-destructive behavior by saying "it doesn't hurt anyone else", because if you really love what is good, you will want to see it produced in yourself as well as others. Besides, by destroying yourself you lose your ability to help other people, and cause anyone who loves you to suffer.
By the same token, it is insufficient if the other person consents, because people sometimes consent to things which are harmful to them. You have to actually decide whether the act of sex would be beneficial or destructive to the other person.
Next comes the biology and psychology. The first fact is that sexual passions cause an intense pleasure, comparable in intensity to addictive drugs. There is nothing inherently wrong in this, but it does mean that we are unlikely to be very sober-minded when making choices about it. Therefore, whatever principles ethics may suggest, they ought to be enforced by clear and explicit social rules in order to avoid ambiguous situations.
The second fact is that we are a species which pair-bonds through sex, conditioned by chemicals such as oxytocin. Therefore, the usual consequence of sex is to create a strong emotional attachment between the two participants. It may be possible to avoid this by deliberately shielding oneself with emotional barriers, but this is unreliable. And what will happen if one person pair-bonds while the other person keeps their reserve?
Worse still, emotional distancing seems likely to lead to a sexuality based not on love but on a sort of contempt for one's own body, or for other people. It's worth noticing in this connection, that lust is not always "love", even if by "love" we only mean romantic affection. Like our sense of humor, lust can even relish cruelty, to oneself or others. There is a reason why certain words for this act have become curse words.
For these reasons, the ethical person will refrain from casual sex, and will only make love in the context of a genuine relationship based on mutual affection and friendship.
Furthermore, these relationships had better be exclusive if they are to be stable. Jealousy is another of those awkward facts about human nature which must be taken into account. It's easy for people (especially immature people who are unaware of their own limitations) to decide that they are sophisticated and mature enough to handle an "open relationship", but the notorious instability of such relationships proves otherwise. Besides, although jealousy is a vice in most contexts, I do not think it is wrong is this context. At least, "free love"—the vision of an idealized (almost communist) human nature in which all can be shared equally among close friends, but no one is entitled to private relationships unsuitable for sharing with others—does not at all appeal to me.
Finally, if these relationships are to result in long-term happiness then there needs to be an explicit understanding that the relationship is intended to be permanent. The alternative is to pair-bond with someone (or more likely, a series of someones), under conditions in which you can reasonably expect that you will eventually be strangers, or even enemies, to that person.
I did not date in college, but I was friends with several couples who dated and eventually broke up. When people are emotionally involved, but not emotionally committed, it is a trainwreck waiting to happen. From an objective outside viewpoint, it seems like the heartbreak outweighs the joy. Modern dating practices are bad enough in this respect, but adding sexual bonding to the mix makes it much worse.
The other awkward little fact about sex is that it makes babies. As commonly practiced, contraception is not 100% successful. Even secular-liberal sexual morality recognizes the problematic nature of an "unwanted pregnancy". Any time a man has sex with a fertile woman whom he is unwilling to marry, he risks making her choose between (a) having an abortion, or (b) having a child grow up with an absent father (and possibly a reluctant mother too).
I believe that (a) is immoral. But rather than get sidetracked about whether there are "secular" reasons for this, I will simply point out that in any case it is a difficult and likely traumatic decision for the woman to make. Another one of those awkward facts about human biology is that a pregnant woman's body is full of hormones trying to get her to feel a strong emotional bond to the unborn homo sapiens growing inside of her.
And as for (b), an ethical person should realize that the interests of children in having loving parents is a thousand times more important than their own interest in sexual or romantic thrills. On the other hand, if in romance you are seeking the deepest interests of the other person, then this interest, like the interest of the child, is best supported by marriage. A gentleman does not use a lady and then discard her when she becomes inconvenient. Nor does he abandon his own flesh and blood.
This post is not intended to say anything against love. Chastity is love: it wills the good of its beloved, by controlling sensual desires, for the sake of the beloved's completeness and integrity.