Responsible Parenthood

Why does the Catholic Church seem intent on everyone having "the children that God commands"?
This statement is somewhat equivocal. The Catholic Church speaks primarily of responsible parenthood, which at all means unlimited procreation, nor a lack of consideration for the difficulties of raising children. The question is that parents use their inviolable freedom with wisdom and responsibility, taking into account their situation and their legitimate desires, in the light of the moral law.
The Catholic Church does not support the idea of fertility at all costs.
The Church praises and promotes the generosity that involves forming a large family. Logically, when there are serious reasons not to procreate, or to space births, that option is lawful. But remains the duty to do so with criteria and methods that respect the total truth of the conjugal encounter in its oneness and procreative dimension, as it is wisely regulated by nature itself in its biological rhythms.

And why not artificial media?
But If what is pursued is the same..., what difference does it make to use natural or artificial methods?
If natural methods were used for an exclusive antinatalist purpose and without sufficient reason, in such cases it would certainly be difficult to distinguish them from artificial means (in terms of their moral value, it is understood).

But the correct recourse to periodic continence differs substantially from contraceptive practices. The artificial means are always directed to remove their procreative virtually to conjugal acts, falsifying them at the root. On the other hand, natural methods, if carried out for just reasons, respect the proper nature of sexuality and its biological rhythms. It is not, therefore, a simple diversity of methods, but an ethical difference of behavior.

Also, natural methods make it easier to respect the other person and his or her body. Temporary abstinence, determined by mutual agreement by man and woman, not only does not weaken love but makes it stronger, freer and more profoundly personal. On the other hand, with the artificial means, it opens the way to that each one, and especially the male, getting used to the use of the contraceptive practices, is unconcerned of the physical and psychological balance of the other person, and comes to consider it as an object of pleasure sex that should always be available for your satisfaction. So many would like to be able to use these natural methods (they are effective, free and without any side effect), but their husbands or wife are not prepared for such a radical change. Contraceptives lead to being sexually available without requiring commitment. Natural methods, however, are compared to a diet: they demand mutual sacrifices, but they strengthen the relationship between husbands and God and favor the same marital relationship.

But natural methods fail...
That's not the way it's been for a while. Chemical or instrumental contraception fails as much or more, even if much less is said, perhaps because it moves more commercial interests (it should not be forgotten that natural methods endanger the fabulous income produced by the contraception industry). A proof that artificial methods also fail is the insistence on abortion or the day-after pill for cases where the condom or contraceptive pill has not produced the desired effect.
Natural methods, in addition to being compatible with all cultures and all religions, are easy to teach and understand. They are free and without any side effects. The freedom and rights of women or husbands are best respected, as they develop a deeper interpersonal relationship between husbands, based on communication, shared decisions and reciprocal respect: they strengthen marriage and therefore family life.
Also, because natural methods help to know the periods of fertility or infertility, they can help the spouses get pregnant. They have made possible the fertility of many husbands who considered themselves to be non-fertile.

Two outbreaks of the same mentality
Some accuse the Catholic Church of actually favoring abortion by stubbornly continuing to teach the moral wrongfulness of contraception. 
It seems strange to me that someone avoids contraceptives, and that avoids them precisely by following the teachings of the church, and that in turn is thinking of aborting later when the same church claims that abortion is a crime.
I think it happens backward. The contraceptive mentality makes the temptation of abortion stronger before the eventual arrival of an unwanted life, and it is clear that the abortion culture is much more developed in environments that reject the teaching of the Church on contraception.
Contraception and abortion, despite being very different nature and moral weight errors, are often closely related, as they are the result of the same mindset: when the life that could spring from the sexual encounter becomes an enemy to absolutely avoid, the abortion is usually the only possible answer to frustrated contraception.

"What about the transmission of aids?"
Some claim the Church to be more understanding. The sequence argumentative is usually that simple: aids are transmitted by sexual contagion, the church opposes the use of condoms, then the church is collaborating in spreading the epidemic.
So he reasoned, for example, a well-known Italian politician, who not long ago asked the Church to change its approach to save millions of aids victims in Africa. Fortunately, there was no need for very elaborate answers to document what was evident to those who know about that drama: the aids epidemic is much stronger in areas where Christianity is less present, and where therefore little can influence the Church in the mentalities and the ensuing behaviors.

As Mia Doornaert explained, if African males were so respectful of the Pope's word that they would, therefore, reject any contraceptive means, they were supposed to be equally strict in following the rest of the teachings of the Church, which preach the monogamy, extramarital purity, and conjugal fidelity, and that is what could slow the spread of the virus. And it doesn't seem that way. It is not serious to blame the Pope and the Vatican for the spread of AIDS, for the same reason that it is not serious to think that the African man, who uses his sexuality according to traditions very far from what the Catholic Church recommends, is waiting for the word of Rome to use or not a condom.

And other than that the condom is much less secure than many thinks, who live daily with the problem of aids know well that to fight this tragedy in these countries must go the way of an education that raises the economic and cultural, the consciousness of the dignity of every man, and especially the valuing of the woman. And to all that they help in a great way the thousands of missionaries who spend there their life creating and maintaining hospitals and schools.

It is very difficult...
The doctrine of the Church on sexuality still seems to many very difficult to follow...
It's a challenge. It offers a model of demanding life but covered with authentic humanity. If you look back on history, and analyze, for example, the figure of St. Benedict and its enormous influence on the cultural roots of Europe, we see that it was a man who marched quite against his time. But his singularity became later the key to a whole cultural and spiritual change on which the Western world of today has been cemented.
Also now, in our time, there are many Christians who do not accept those models of sexual permissiveness, even if they are so widespread that we almost impose. They seek new models of life in the faith. They may not yet draw the attention of public opinion, but over time, the future will recognize the importance of what they are doing.