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No, it (original sin) is the means by which all men are fallen. The reason is so that we must choose and achieve Salvation.

That is not what Scripture says. That doesn't even make much sense.

If the "reason" all men are fallen is that we must choose salvation, and yet some men DO choose salvation, then all men are not fallen.

You've negated your own assertion.

"Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned" -- Romans 5:12

Besides, New Advent agrees with me and Paul...

Original sin may be taken to mean: (1) the sin that Adam committed; (2) a consequence of this first sin, the hereditary stain with which we are born on account of our origin or descent from Adam.
From the earliest times the latter sense of the word was more common, as may be seen by St. Augustine's statement: "the deliberate sin of the first man is the cause of original sin" (De nupt. et concup., II, xxvi, 43). It is the hereditary stain that is dealt with here. As to the sin of Adam we have not to examine the circumstances in which it was committed nor make the exegesis of the third chapter of Genesis.