Q. Why is it that the church has latched onto the modern concept of dating instead of following the Bible’s command of betrothal?
I’m not entirely sure what you mean by “betrothal,” but in any event, I do not believe personally that the Bible specifies one particular way of finding a spouse. Instead, I think we see the people in the Bible following the customs of their own cultures in this regard, and the Bible warning against ways that those customs could be abused.
In some cases we see arranged marriages. One well-known example is when Abraham sends his servant back to the family homeland to get a wife for Isaac from his own “country and kindred.” Isaac is expected to marry the woman the servant comes back with.
However, in other cases, even though the parents would ultimately arrange the marriage, the child seems to have some say in the matter. For example, Samson says to his parents, “I have seen a Philistine woman in Timnah; now get her for me as my wife.” The parents don’t reply, “Now we’re the ones who will choose a wife for you.” Instead, they reply, “Isn’t there an acceptable woman among your relatives or among all our people? Must you go to the Philistines to get a wife?” So they don’t object, in principle, to Samson letting them know whom he wants to marry. They object to him wanting to marry a Philistine, but they seem open to accommodating his choice of a wife as long as he wants to marry a fellow Israelite.
In the New Testament period, marriages took place under the laws and customs of the Roman Empire. In those circumstances, while parents arranged most first marriages for their children, the children had the right, on certain grounds, to refuse to marry someone the parents had selected. Moreover, many marriages ended in divorce or after the death of a spouse, and men and women had much greater freedom to choose a spouse when remarrying. One possible meaning of one of Paul’s commands in First Thessalonians is, “Each of you should know that finding a husband or wife for yourself is to be done in a holy and honorable way.” If that is the meaning, then this shows that people in this time and culture could choose their own spouses, whereas in other biblical cultures, parents arranged marriages.
So, as I said, I think the Bible allows for a lot of creative cultural freedom in this regard. When it comes to dating, I would not say that the Bible forbids it, but rather that people should follow biblical principles to make sure that dating is done in a healthy and God-honoring way. For example, I personally believe that anyone a person might get into a dating relationship with should be a potential spouse. This means that for a follower of Jesus, that person must also be a follower of Jesus. (I say that people should only get into a dating relationship with a potential spouse because people who date can form strong emotional attachments, and those can lead to marriage, even if the people dating didn’t have that in mind to begin with. A simple way to put this is, “Don’t play with fire.”)
I would also say that people who date should be careful to maintain healthy emotional and physical boundaries, appropriate to the commitment level of dating. They are not married. They are not engaged. So they should not build their emotional lives around one another, and they should act toward one another in a “holy and honorable way.”
In short, I personally believe that dating is one way in which people in some cultures go about looking for a spouse. Like all such ways, it can be done in a healthy way or in an unhealthy way. The Bible gives us principles to show us how to do it in a healthy way. But the Bible does not privilege one cultural practice over another.
Good Question 
It all depends on just what you mean by “dating.” Even today, everyone has a different definition to dating. It can be as benign as a courtship of “flowers…dinner…movie…dancing” to the extreme of a night of debauchery and expected sexual encounter with no strings, or emotions attached. Even the word “Friendship” today has taken a beating with the concept of “friends with benefits.” So you may as well ask “does the Bible forbid Friendship?” Dating in the traditional sense is a precursor to marriage. The courtship allows the couple to ascertain their compatibility as a married couple with the prospects of cultivating love between them. Taking into consideration their personal values and their responses to everyday events in life. It is a very delicate process left best to the mature at heart and should be treated with respect.