Here are just a few quotes from the Pontiff:
Socialism considers the individual person simply as an element, a molecule within the social organism, so that the good of the individual is completely subordinated to the functioning of the socio-economic mechanism. Socialism likewise maintains that the good of the individual can be realized without reference to his free choice, to the unique and exclusive responsibility which he exercises in the face of good or evil. Man is thus reduced to a series of social relationships, and the concept of the person as the autonomous subject of moral decision disappears, the very subject whose decisions build the social order. From this mistaken conception of the person there arise both a distortion of law, which defines the sphere of the exercise of freedom, and an opposition to private property. A person who is deprived of something he can call "his own", and of the possibility of earning a living through his own initiative, comes to depend on the social machine and on those who control it. This makes it much more difficult for him to recognize his dignity as a person, and hinders progress towards the building up of an authentic human community.
In contrast, from the Christian vision of the human person there necessarily follows a correct picture of society. According to … the whole social doctrine of the Church, the social nature of man is not completely fulfilled in the State, but is realized in various intermediary groups, beginning with the family and including economic, social, political and cultural groups which stem from human nature itself and have their own autonomy, always with a view to the common good.
I believe that anarchism is unstable in practice.
Why haven't even one private defense agency has arisen to protect those believing in an anarcho-capitalist system? You can't "blame" the existing governments for not allowing private defense agencies as they are known to use force unjustly to maintain their monopoly. The real test of the system is not when there is no opposition to it or in absense of injustice. People have gained independence and freedom from tyrannical governments all the time. But invariably the result was not a anarcho-capitalist system but another government. For example, when India gained independence from British Raj, why it got split into multiple monopolistic governments instead of multiple private defense agencies?
Private defense agencies are perfectly capable of giving protection to its members. But invariably, there will be free-riders. Those non-members who receive benefit because of the law and order maintained by private defense agencies will not be under any obligation to pay the agency. Otherwise, the agency will be nothing but a monopolistic government. I think this situation prevents private defense agencies from arising. Or even if they arise, they degenerate into monopolistic governments.
Apart from non-members who intentionally refuse to pay for the benefits, free-riders can also arise if one private defense agency is so powerful as to automatically defend from external agression the members of the other private agencies in the same geographic area. In that case, its members will have to pay more fee to cover the expenses of developing and maintaining the extra power. Other private agencies can avoid doing the necessary investment for defense of their members and thus can afford to charge less. In that case, if the private agency refuses to force non-members (including members of other agencies) to pay for the defense then it will see a steady decline in its paying membership and ultimately bankrupt itself. If it forces non-members to pay for the defense from external agression then it becomes the government.