Parents have obligations to their children because parents are causally responsible for placing their children in a state of peril as a result of creating them. Parents are responsible whether they intended to create children or not, since one must accept the reasonably foreseeable consequences of one's actions as chosen, even if those consequences were undesired.
The act of placing a child in a state of peril (by creating the child) makes the parents liable to remove the child from peril. Failing to do so is tantamount to an act of aggression. In this way, parents have an enforceable positive obligation towards their children.
Fulfilling this obligation turns out to be an enormous responsibility, since removing a child from peril involves whatever actions are necessary to raise that child to the safety and self-sufficiency of adulthood. This comprises countless millions of small acts required to keep the child safe, clothed, fed, sheltered, educated, and so on.
Since a new human being is created when two gametes fuse, it is the voluntary act of making one’s gametes available for fertilization that gives rise to parental obligation. The obligation is incurred whether one makes one's gametes available through sexual intercourse, which entails the natural possibility of fertilization, or through assisted reproductive technologies such as in vitro fertilization (IVF). James Lindemann Nelson explains the basis for this act being the source of causal obligation:
The making available of one’s gametes is an act highly proximate to conception, and, in concert with the other parent’s actions, is jointly sufficient for it. Our practice is generally to take proximity and sufficiency pretty seriously; a pair of coordinated actions which were proximate to and jointly sufficient for some event, and were not the result of forcing or fraudulent action on the part of others would be hard not to see as the cause of the event in question. Becoming a parent generally fits this model.
A clear logical implication of the principle of parental obligation is that parents have obligations to every embryo that they create, since every embryo is the result of the voluntary act of making their gametes available for fertilisation. This also entails that parents have obligations to every embryo created using IVF.
Although it is technically possible to transfer every embryo created during IVF, the process typically results in many more embryos created than are used. One cannot be precise about how many embryos are unused, since this data isn't directly available, so it can only be inferred or deduced from other statistics. An AI asked to make an estimate gives a figure of more than 95% of IVF treatments resulting in more embryos created than are transferred.
What happens to these unused embryos? They are either discarded (destroyed) or cryopreserved indefinitely. Destroying an embryo entails the killing of a child that the parents have responsibility for. This is an act of aggression that is unjustifiable and incompatible with the obligation of the parent to remove the child from peril.
Of those embryos that are preserved, some may eventually be donated to others, destroyed, or remain frozen with no clear future. Donating or selling an embryo is an unjustifiable abandonment of parental responsibility. The child has a claim on the parent and the parent cannot just sell or give that child away to someone else because parents cannot give up their obligations. Leaving an embryo frozen to an uncertain fate is a clear failure to fulfil the obligation of removing the child from peril.
Some proportion of IVF cases rely on gametes purchased from (or donated by) others who will not parent the resultant child. Since making one's gametes available for fertilisation is the act that gives rise to parental obligation, gamete sale or donation cannot be justified because it constitutes an unjust abandonment of parental obligation.
All these typical practices during IVF are incompatible with parental obligations. Although IVF could be compatible with parental obligations if every embryo was transferred, this is not done in the vast majority of cases. Additionally, some proportion of IVF cases involve gamete sale or donation. Therefore, IVF as currently practiced is almost always incompatible with parental obligations.
For a more detailed explanation of the principle of causal parental responsibility see my JLS article here.