One nature does not make billions of beings one being.
What I mean by being is precisely the same thing as everyone else means by persons, as they are synonyms. Trinitarians must parse such synonyms to support their wholly doctrine.
Jack and Jill are 2 beings. Father’s and son’s are 2 beings.
If that's what you mean then that doesn't contradict the Trinity though, and I would assert it with you. Jack and Jill are two persons. The Father and Son are two persons. One nature does not make many persons the same person.
We don't assert that at all. Do you think Trinitarians are Sabellians or something? Asserting that they are two beings is even in the Trinitarian Fathers if I recall correctly, also words such as "existences" and so on to be made synonyms with person, I have no problem with that, what we have a problem with is dividing the natures in either case.
So it seems to me that this opening statement does not go against the Trinity. Neither do a lot of things in fact, we believe in the Monarchy of the Father (by which St. John Chrysostom said on account of this we would not even contradict one who said the Father was greater than the Son if this is what they meant, that the Father is the sole principle of divinity), so we can rightly say that the Father is "only God" or is "God" and Christ is "Lord." We in fact affirm based on this that there is One God (the Father). Is generation impossible for Him? It does not contradict itself so it doesn't seem to be impossible, but that is not the line of attack on the Trinity anyway so it's irrelevant.
Human fathers and human sons being two beings/persons (you equated them) also to us proves our point. One generated the other, a father does not generate a giraffe or a dolphin but a son which has the same nature as the father (although the mode of generation differs from the Trinity of course). Yet they are two by being two distinct persons, but they are one in regards to their nature (what they are, a human is not a dolphin, different natures).