Atheists, tell me, a Roman Catholic: why should I become an atheist?

[Ignorant]

help me understand how to determine a statement to be infallible

Sure thing. Here's what Vatican II said:

"And this is the infallibility which the Roman Pontiff, the head of the college of bishops, enjoys in virtue of his office, when, 

1. as the supreme shepherd and teacher of all the faithful, who confirms his brethren in their faith, 
   
2. by a definitive act 
   

he proclaims a doctrine of faith or morals."
-Vatican II, Lumen Gentium, Ch. III, n. 25 (numbering mine)

So it must be clear in the dogmatic statement that the Pope is 1) speaking from the authority of his office, and 2) is acting definitively (i.e. an irriformabile way)

---

Here is an example:

"By the authority of Jesus Christ our Lord, of the Blessed Apostles Peter and Paul, and by our own: "We declare, pronounce, and define that the doctrine which holds that the most Blessed Virgin Mary, in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ, the Savior of the human race, was preserved free from all stain of original sin, is a doctrine revealed by God and therefore to be believed firmly and constantly by all the faithful"
-Pius IX, Ineffabilis Deus, 1854