Loaded question, my apologies.
I grew up on a ranch, and I typically envision treatment of slaves in the South like I would envision treatment of cattle by ranchers, which I understand to be a pretty apt comparison. Ranchers are actually really selective with the way their cattle breed (they typically get vets to perform abortions if there's an unwanted pregnancy), so I was curious to see if slaveowners were the same way with enslaved African Americans, or rather, how different it was.
In some ways, your interpretation of slavery is correct. This is certainly the attitude that many white planters had towards their Human property. Like animals, slaves in the antebellum south were not just a source of cheap labour, but a capital investment; in economic terms, slaves had value both as labour and as a kind of high liquidity asset. As as a source of labour, large-scale planters wanted an abundance of fit, healthy slaves to maximise their output; as an investment, the capacity of slaves to reproduce meant that they could also create new sources of capital, much in the same way livestock can.
We are talking, however, about individuals who clearly had Human agency - even in the context of slavery. Though planters may have in many ways treated their slaves like cattle, they were aware, whatever language that they may have used, that the situation was not so simple and straight-forward. Whilst there is some evidence that suggests some plantation owners engaged in practices akin to forced breeding, selecting slaves and forcing them to have sex, they very much appear to be exceptional extremes; the recollections in slave narratives usually imply when this did take place, it was much more about power and domination than about selective breeding in a 'scientific' way.
Much more common in the historical record is evidence of white male planters - or their relations and employees - forcing themselves sexually upon slave women against their will, at times taking them as de facto concubines. Often, these unions would result in the birth of children (sometimes several children) who would, as far as the law and planters were concerned, be slaves themselves. The treatment of these women and their children in these circumstances could vary considerably from plantation to plantation - in some situations, they might be treated markedly better than their fellow slaves. In others, the same, or worse.
Overwhelmingly though, the black experience of the family in slavery is a remarkably strong one - though quite how strong is still very much a subject of ongoing debate. Certainly slaves tried earnestly to build real, meaningful family units; they would seek to marry who they wanted from within their own or neighbouring slave communities, and earnestly seek to raise their children on their own terms, often with the assistance of grandparents where family units had been preserved. One of the major concerns slaves had about their condition was that it was so easy for their owners to casually disregard and break-up families; familial and community bonds were enormously significant to many slaves.
The extent to which black family life and identity could develop, however, was heavily limited by the conditions of slavery imposed by the planter class. On those plantations where owners did practice extreme methods of sexual control and coercion, opportunities were obviously significantly more limited; many of the planters who did give their slaves freedom to marry granted it only within the confines of their own plantation. Across the plantation economy, slaves were workers first, an investment second and everything else last - the entire system relied on providing the means to achieve total domination and control of slave life, and family life was no exception. Families were always at risk of violence - physical or sexual - and disruption.
In terms of abortion, I am not aware off the top of my head of any instance were planters enforced abortion - killed young children, certainly, or accidentally induced miscarriage through abuse, but not aborted in such a methodical fashion. It was slave women who we find tried to make use on occasion of contraceptive or abortive techniques; in those cases, that was usually as an act of resistance, either to avoid pregnancy by an abuser or to refrain from bringing more children into the condition of slavery.
In most cases, the slave experience of family was real, consensual and meaningful, but enormously fragile - the extent to which a family unit could thrive was largely at the mercy of the planter class, and the system of slavery itself left little room for family life, particularly in the intensive agricultural economy of the Lower South. The kind of extreme methods of control you describe by the planter class probably did occur but were rare; more 'mild' methods of coercion and violence were more likely to take place (including sometimes positive incentives for reproduction, like a reduced workload for mothers although, again, these measures were not wide-spread).
Selected Bibliography
EDIT: Have to dash but I'll finish up the bibliography with a few more bits later!
So my only in-depth experience with individual antebellum slave owners is Drew Gilpin Faust's book on James Henry Hammond, so here it goes.
Slaves would marry who they wanted, with or without the permission of their master. It was not uncommon for masters to have a say in who their slaves married. They were not adverse to breaking up families by selling members of the family. Some owners, such as Hammond, as had naming rights of any newborn slaves.
I don't think plantation owners went as far to "breed" slaves selectively, at least none that I know of. It could have happened but I don't think it was widespread. I also haven't heard of abortions on unborn slaves.