“because man would be poorer in every sense”. (source)
1. Spiritual Poverty is Worse than Material Poverty
In other words, "man shall not live by bread alone" (cf. Matt 4:4). The artworks of the Vatican are the preserve of all the world and all of us would be immeasurably poorer if they were to be sold to some private collector, never to be enjoyed by the Faithful again. The great artists that made these masterpieces made them to honor and glorify God and to save the souls of those who, through viewing them, would grow closer to God and who would be brought to repentance for their sins. Having once stood in front of Michelangelo's Last Judgement as an unbeliever, I can personally testify the power good art can work upon a even a closed and dry soul. It is this poverty, spiritual poverty, which Mother Teresa (who lived and labored among the economically poorest of the world) called "the worst poverty and the most difficult to overcome." (source)
2. What Would Jesus Do?
The attitude of the man who wants to sell off man's patrimony for a few loaves of bread isn't anything new, Jesus Himself faced such an objection from within His chosen apostles
(Jn 12: 1-5)To Judas, the progenitor of our modern critic, Jesus has no kind words,
“Let her alone; why do you trouble her? She has done a beautiful thing to me" (Mk 14:6)As too have the greatest artists in the history of man, who have spent their time and treasure doing "beautiful things" not for overly wealthy private art collectors, but for Him.
Jesus then goes on to point out the ultimate futility of trying to sell off all things of beauty for bread, reminding His disciples that
We will never eliminate poverty this side of the parousia and despoiling God's house in a vain effort to is clearly not commended by Christ.
3. God Doesn't Will It
In fact, it seems God (as can be seen in His plans for both the Tabernacle in the Wilderness and the Temple of Solomon) isn't a big fan of depriving His people of beauty,
The house which King Solomon built for the was sixty cubits long, twenty cubits wide, and thirty cubits high....
A False Dichotomy
None of that, of course, is to downplay the importance of feeding the hungry (something Jesus also demands)
‘Truly, I say to you, as you did it not to one of the least of these, you did it not to me." (Matt 25)Which ends up being another example of the classic Catholic principal of "both/and" not "either/or" (which is the hallmark of heresy). We are not called to either beautiful churches or feeding the poor, but to both beauty and charity. For, in the final analysis, beauty is a form of charity, it is feeding the spiritually poor.
The Best Answer
But maybe the best answer is to ask whoever raises this objection which of their personal effects they're in the process of selling to feed the poor. For some reason I doubt their BMW, shoe closet, golf clubs, iPhone, etc is doing much to alleviate the spiritual poverty of the world, unlike the Vatican's art.