PRIVAte and dePRIVE are etymological siblings, from the Latin "privare."
In simpler, less complex societies, greed and selfishness are usually negatively sanctioned while generosity and giving are usually positively sanctioned. To keep a communally needed good private, separate, to myself, is to deprive others of a basic good they need to survive. In such simpler societies, the primary unit of survival is the group, not the individual (as is the case in a "band of brothers").
This common good is consistently DEMANDED throughout our books of religion, particularly our Abrahamic religions. Adherents are continuously warned they will be rejected by their god if they ignore the common good, if they do not care for the poor, the widowed, the orphaned, the elderly, the sick, the imprisoned, etc.
Our integral sciences support the same. To be healthy, to remain functional, a society must balance the rights and responsibilities of individuals. As an individual, I have basic rights. As a member of larger wholes (a marriage, a family, a community, a nation, a global community, etc.), I have responsibilities.In our far more complex, far more individualistic society, I am fortunate to have far more private goods than many others. Therefore, I also have far more responsibilities to the larger wholes of which I am a part.
In the terms of the great anthropologist Ruth Benedict, one of the two individuals who inspired Abraham Maslow's consideration of "higher needs," societies are synergic, have high synergy (what is good for a part is good for the whole and vice versa) or nonsynergic, have low synergy (what is good for a part is NOT good for the whole).
With our emphasis on individual rights ("Second Amendment" private, unregulated ownership of assault rifles, for example) without a balancing consideration of responsibilities (the "General Welfare" of the Preamble to our Constitution, for example), we are presently extremely nonsynergic. Which does not bode well for the continuation of our nation, to say nothing of those who are egregiously deprived (the hundreds of Americans who die every day because they do not have access to health care, for example).
We have become a cancerous society, with individual parts (the 1%, the serial killer with an assault rifle, the Tea partier demanding delaying "Obamacare" in exchange for a Continuing resolution in the House, etc.) destroying other individual parts and groups of the greater whole of which we are all parts. And if this is not moderated, the cancers within/among us will eventually destroy their host (our communities, our state and/or nation, our earth).
The common good is not only common sense, it is right and moral and scientific.