When you breed a mare, you want the result to be something that someone else would want should you ever have to find it another home.
Agree with this 100%. I bred my arab mare. She is registered, with a decent pedigree, very good conformation over all, extremely healthy and the best saddle horse I've ever owned. She is bred to a thoroughbred stallion who's disposition and breeding are excellent, conformation is very good and has a decent record on the track. I chose this cross because 1) its a popular cross for various English disciplines, 2)its a cross well suited to endurance racing, which I enjoy, 3) the mare and stallion complement each other very well, where he is not ideal, she is strong, and vice versa, and 4) its not terribly common around here, and I know there is a market for it. I want to keep this foal, but life happens, and I really have no idea what the future holds. The most responsible thing I can do as a breeder is to breed something as desirable as possible, to help ensure its future.
I will also say, Despite the positives of the situation, I very nearly did not breed her, for various reasons.
If you breed your mare, I highly recommend saving, and breeding to the best possible stallion you can afford, ideally with color(such as dun factor and/or a dilute) as well as a nice pattern, and a show record, with of course the essential great conformation, disposition and breeding. You are going to find a colored, paint pattered half arab with a recognizable sire much more marketable.