פירוש על קידושין 36:9

The problem is that if designation counts as kiddushin, then we still need to ask how could her father again sell her. Once a girl has been betrothed, she may no longer be sold.

We could try to get out of the problem by saying that while her father cannot sell her after he accepts her betrothal, he can sell her after she accepts her own betrothal from her master (designation). But then we could say the same thing if designation effected marriage—he can’t resell her after he marries her off, but he can after she marries herself off. So this again leaves us with no answer to our question.