The previous answers assume that there's a 50% chance on any flip of getting heads. But what if we're using a "trick" coin that, say gives a 99% chance of heads? In that case, we might have a realistic hope of getting all heads if we flipped 10, 20, 50, 100 or even 200 coins.
But we would still have no realistic hope for that 106 billion. The odds of getting 106 billion heads even with a coin that came up heads 99% of the time are over a billion to one.
Indeed, even if we define "realistic" conservatively as having, say, at least a 1% chance (which might be "realistic" but is still pretty small), then to have a realistic hope of getting heads on all 106 billion flips, the chance of getting heads for one coin would have to be on the order of 99.9999999%, give or take a few nines. That's not certainty, of course, but it's as close to certainty as virtually anything ever gets.
If I (being the ingenious and clever sinner that I am) use a magnet on a slot machine, giving me a 99.9999999% chance that I will come up a winner, in common-sense language, I would be perfectly within my rights to say that I know or I'm certain that I will win.
I would.
On one estimate, there have been approximately 106 billion human beings born on earth since 6,000 BC.
To say that we have a realistic hope that all of those were or will be saved, then (see above) there would have to be at least a 99.99999999% chance for each one of us, considered individually, to be saved.
It follows that there would be only a .00000001% chance (if that) for each one of us to go to Hell. To claim that that amounts to a "real possibility" is an abuse of common-sense language.
The main point is that the "realistic hope" of universal salvation contradicts the "real possibility" of individual damnation. You just can't assert both things at the same time. Or, rather, if you do, you're talking nonsense.
A subsidiary point is that Barron's "realistic hope" makes him for all extents and purposes a universalist. Or if he is not technically a universalist - for each person, there's a whopping .000000001% chance that he will not be saved - then he's a watered-down universalist. His giant frothing mug of universalism contains one atom of water.
Lastly, of course, those incredibly low "odds" for damnation are in complete contradiction to the words of Jesus, the opinions of the Church Fathers and the traditional formulations of the doctrine of hell by the Church.
I hope I'll be saved. I hope you'll be saved. I hope that that drunken, abusive guy who had a fatal heart-attack while in bed with his mistress will be saved. If I am a true Catholic and a magnanimous fellow, then I hope (or should hope) that Napoleon, Stalin, Hitler and Pol Pot will be saved. Perhaps in some sense it is "realistic" to hope for Napoleon, etc. After all, God will forgive anyone if they sincerely repent.
But it isn't realistic to hope for all of them to be saved in sum. If Christianity is true, then they won't be. Not all of them.
Maybe Barron should have taken a statistics course.
Why does all of this matter? Well, obviously, logic matters and the truth matters, whatever one's purpose.
But beyond that, I think what we might call Barron's trickery is obvious. And I do mean trickery. It is incomprehensible to me that a man of at least middling intelligence, such as Barron, cannot see what he is doing. Obviously, Barron thinks scaring people with Hell is medieval or low-class or fundamentalist or whatever. Respected contemporary theologians or apologists just don't do it. And you know how much he wants to be respected.
Or to be more charitable, perhaps he thinks scaring people with Hell just won't work to convert them or get them to stay. (As I argued a few days ago, there's no evidence for that, whatsoever. Indeed, the opposite is much more likely.)
But he can't explicitly ditch Hell since it's such an obvious Church teaching. Hence, the bait and switch.
Traditional Catholicism is often criticized for putting inordinate importance on being Catholic. But of course, for the Church, being Catholic has always been a means to an end. The end (or at least one of the primary ends) is the salvation of one's soul. Or as the Church used to put it for the first 98% of its existence before people like Barron came along, the salvation of as many souls as possible.
The irony is that it's the anti-traditionalist Barron who really seems to have the fetish for being Catholic, without really telling us what it's for. By strongly implying that everyone will be saved, he's jettisoned the practical importance of saving people, and thus eliminated at a stroke what the Church historically affirmed as its most important mission.
And he calls himself an evangelist?