The Church has always supported the acquisition and possession of

“Now, when man thus turns the activity of his mind and the strength of his body toward procuring the fruits of nature, by such act he makes his own that portion of nature’s field which he cultivates—that portion on which he leaves, as it were, the impress of his personality; and it cannot but be just that he should possess that portion as his very own, and have a right to hold it without anyone being justified in violating that right. ”
St. Pius X wrote in 1903, that all private property “is an incontrovertible natural right; and everybody can dispose reasonably of such property as he thinks fit.”
The Catechism of the Catholic Church (¶ 2402) also affirms the right to private property as a human necessity, saying: “the earth is divided up among men to assure the security of their lives, endangered by poverty and threatened by violence. The appropriation of property is legitimate for guaranteeing the freedom and dignity of persons and for helping each of them to meet his basic needs and the needs of those in his charge.”
Tragedy of the Commons
The idea of the “tragedy of the commons” is an observation widely attributed to Oxford economics Professor W. F. Lloyd in his Two Lectures on the Checks to Population (1833). The problem itself is at least as old as agriculture.

Suppose villagers share common pastureland in which each sheepherder has the right to graze his sheep. The land will support only so many sheep. Nonetheless, each herder knows he can increase his profit by adding sheep to the common pastureland, even though the land will—at some point—be damaged by overgrazing. A selfish herder will not care, because he can retain all the extra profit from his overuse while sharing the costs of overuse with his neighbors. As more sheep herders take advantage of the arrangement, the land is quickly brought to ruin.
This problem exists whenever the rights to scarce resources are shared. It may involve hunting, fishing, water or logging rights. It may arise over the use of radio frequencies or advertising space; or where vandalism and littering occur in public parks and restrooms.
There are two main solutions to the problem. The first is coercion by government which typically addresses these problems with laws, hoping the threat of punishment will settle the matter. Often it does not. The other solution is private property.
St. Thomas Aquinas on private vs common property:
While Professor Lloyd may have set forth the problem of common property in the modern setting, it would be surprising if the phenomenon had not been recognized far earlier; and so it was—600 years earlier—by St. Thomas Aquinas in his Summa Theologica, in which he discusses the irresponsibility of individuals toward the common use of property:

“Every man is more careful to procure what is for himself alone than that which is common to many or to all: since each one would shirk the labor and leave to another that which concerns the community, as happens where there are a great number of servants.” [ST II-II, Q. 66, Art. 2.]
A man is more careful with his own property, but less so with property that belongs to the community. Even an honest man who would not overuse or take more than his share is unlikely to go out of his way to police everyone else’s use of the resource. Not so with private property. The private owner will not ruin his own pasture, water well or stream just to make more profit this season. Nor will anyone else, for landowners will naturally tend to preserve and protect their property from trespassers. He understands that while the benefits of overuse are his alone, so are the costs. This is enough to cause most people to take reasonable care for their property.
Thomas Aquinas also notes that common property is often neglected and leads to disagreements:
“[H]uman affairs are conducted in more orderly fashion if each man is charged with taking care of some particular thing himself, whereas there would be confusion if everyone had to look after any one thing indeterminately.”
“A more peaceful state is ensured to man if each one is contented with his own. Hence it is to be observed that quarrels arise more frequently where there is no division of the things possessed.”
The tragedy of the commons—in St. Thomas’s view—is that it creates discord, neglect of the common resource and its eventual destruction. Libertarians agree with St. Thomas that the better solution to these ills is the personal responsibility that naturally accompanies the private ownership of property.