There's absolutely nothing wrong with dating while sober, but many people in recovery choose to delay any romantic relationship for at least 12 months after completing a drug and alcohol rehabilitation program in an effort to protect their sobriety. Recovery, as any sober person will attest, is hard work; and like any form of hard work, a little help goes a long way. Some of that help comes in the form of post-care support, such as 12-step groups and Alcoholics Anonymous, but the investment and commitment of others in the person's life goes a long way. This means that friends and family should, when possible, participate in the activities that the person considers most beneficial to recovery.
By extension, the presence of a partner will also be an enormously reaffirming and inspiring boost to the person's sobriety. A moderate drinker shouldn't have to stop drinking to be with a sober person, but understanding that there are some unique aspects of dating someone in recovery, such as temporarily disconnecting from some activities and participating in others (such as attending support group meetings), will lay the foundation for a healthy and prosperous relationship. Any relationship requires sacrifice and commitment. A relationship between someone who likes to drink (and gets drunk from time to time) and someone who can't drink at all will have to achieve a very delicate balance between giving and receiving.
Sometimes, the two members of the couple will need to have different plans for a night. Sometimes, the sober couple will have to prioritize sobriety over the relationship. There's no guarantee that sober dating will always be fun or easy; but if both partners are willing to make it work, then they can find true happiness in each other. That feeling can be a drug in and of itself, not found in sober life (and especially in sober relationships).
As most people in recovery will say, being sober involves living in a world that isn't sober, and a dating scene that is intrinsically linked to drinking alcohol to make things happen. If you're not honest with the person you're dating about sober living, it could come out later and end up causing problems in the relationship.