Why do you think mothers can't give birth to their own children in The Giver?

I think there are a few reasons women do not give birth to their own children in The Giver.  These reasons are to allow the leaders of the community to more easily maintain control over the community.

First, if women gave birth to their own children, they would be having sex with partners.  We can infer that there is no sex in the community because everyone's sexual desire is repressed with drugs the minute it surfaces. Stirrings must be reported immediately, and then the "treatment" begins. (There is no discussion about how Birthmothers are impregnated, but I have always thought that it is through artificial insemination, rather than through sex.) If people have sex, the leaders begin to lose control. People will want to choose their own mates and sexual jealousy might surface.  And when people have sexual desires, they are less inclined to follow rules, for example, the rules on sameness for clothing, as some people would want to dress more provocatively. They might commit adultery. They might not be so productive at work, flirting or sneaking out for a tryst.  One reason this society functions as well as it does is because there is no sex. People's energies are channeled away from sex to productivity.  All in all, allowing sex would make the population much more difficult to control and channel effectively.

Second, if women gave birth to their own children, they would love them, as would their fathers, no doubt, and this, too, would act to weaken the leaders' control.  Love is an emotion that is repressed in the community, mocked actually. It is not clear whether the repression is the result of some drug or simply some very effective brain-washing, but no one but the Giver and Jonas seem capable of this emotion.  As parents are "assigned" children to whom they have no biological ties, they think of parenting as just a job, and they do not have the same stake in the game.  Biological imperatives make us fight for our children, seeking advantages for them, even at a cost to others sometimes, and this dynamic is not operative the way things are arranged in this community. (I hasten to say that this is not like adoption, in which case parents want the child as part of the family and behave just like biological parents.)  Mothers and fathers might question the jobs to which their children were assigned. They would be likely to want to dress them more nicely, or at least differently from others.  They would want educational advantages for them. They would want to buy them books and nicer toys. They would care more about the success of their children than about the community as a whole.  All of this would mean the leaders' loss of control.  Sameness would never be the same. 

In separating parenting from sex and making it a job, an assignment, not a choice, the leaders have found an effective means to exert control over the populace. This eliminates sex as motivation for anyone's actions or behavior. And it eliminates love, which is an exceedingly difficult emotion to control.