Health Justice should be a priority of governments.
Justice = giving the person what is due to him.
The question comes in whether a person is
owed the servitude of a doctor. Whether a person is
owed the fruits of your labor, my labor, and everybody else’s labor to pay the doctor for the doctor’s labor (if the doctor is not
obliged to provide his labor outright).
In other words, it comes down to the rights of private property. Does justice
demand that you, I, and everybody else have a portion of our property confiscated
in order to pay for services provided to somebody else.
The answer to that question is no.
If the answer was yes, then that sets up division of classes which is a violation of the principle of solidarity.
Where the obligation comes in is through the principle of participation. I have an obligation to voluntarily share my excess with those who have need. To quote Pope Leo XIII

rivate ownership, as we have seen, is the natural right of man, and to exercise that right, especially as members of society, is not only lawful, but absolutely necessary… True, no one is commanded to distribute to others that which is required for his own needs and those of his household; nor even to give away what is reasonably required to keep up becomingly his condition in life, “for no one ought to live other than becomingly.” But, when what necessity demands has been supplied, and one’s standing fairly taken thought for, it becomes a duty to give to the indigent out of what remains over. “Of that which remaineth, give alms.”
It is a duty, not of justice (save in extreme cases), but of Christian charity - a duty not enforced by human law…
That is the principle of Participation working to support Solidarity, recognizing the Universal Destination of Goods and the Preferential Option of the Poor.
Big government solutions take us the opposite way of establishing a sense of solidarity among peoples, recognizing the universal destination of goods and the preferential option for the poor.
No less an authority that Cardinal Turkson, President of the Pontifical Council for Justice and Peace, has made that very point:In a recent interview with CNA, Cardinal Turkson said he has learned from past experience that the Church’s justice and peace terminology often needs clarification for an American Catholic audience. Key terms used by the Vatican — such as “social justice” and “gift” —
are not always understood the way the Vatican intends, he said.
"We found out that some of the vocabulary which is just taken for granted and used freely may not always have the same sense or may have had some nuances which sometimes are missed because of the way the terms are used in the American political context,” Cardinal Turkson said in a Jan. 12 interview at the council’s offices in Rome.
(snip)
Cardinal Turkson explained that in the Church’s thinking, social justice involves
citizens’ obligations and responsibilities to ensure fairness and opportunity in their communities and societies.
While this may include the adoption of specific government policies and programs,
the emphasis in Catholic social teaching is on the obligations that flow from citizens’ relationships in societies.
(snip)
“Respecting, understanding and fulfilling those demands constitute our justice,” he said. “It would be useful if we just observed our sense of justice as our ability to fulfill the demands of the relationships in which we stand.”
This is in contrast to socialism, he explained, which is an ideology in which private property and private interests are totally placed in the service of government policies.
What the Pope proposes in “Caritas in Veritate,” said Cardinal Turkson, is “achieving the common good without sacrificing personal, private interests, aspirations and desires.”
Cardinal Turkson said the Council was also surprised that the Pope’s concept of the “gift,” was perceived in some circles as encouraging government welfare handouts.
In “Caritas in Veritate,” Pope Benedict described the concept of “gift” as a way to understand God’s love for men and women in his gift of life and his gift of Jesus.
You may be interested in reading the Zenit inverview with His Eminence from last November (
part 1 and
part 2) as well as the
CNA article summarizing their Jan 2011 interview with him.