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The obvious solution to this problem is simply to look at the original Hebrew. But that is where the problem begins. The medieval Hebrew Masoretic manuscripts read "he shall crush." (However, there are two Hebrew manuscripts that read "she shall crush.") However, there is good reason to doubt the majority Hebrew reading of "he shall crush."
Our three best Jewish witnesses to Gen 3:15 interpret the passage as "she shall crush." These are Philo Judaeus, Josephus the roman historian, and Moses Maimonides, the great medieval Jewish philosopher. Philo argues that the Hebrew parallel poetry of Gen 3:15 demands the reading of "she shall crush." Josephus, also writing in Greek, describes the passage for us as reading "she shall crush." Then last of all, Maimonides also states that Gen 3:15 teaches that the woman shall crush the head of the serpent.
So then, these three great Jewish scholars testify to the traditional Catholic reading of the Latin Vulgate. Why are the Hebrew manuscripts that we have today different from these ancient Jewish witnesses. The answer is that the Masoretic manuscript tradition has been corrupted - something claimed by the both the Eastern and Western Fathers throughout the centuries.
LXX - He
Dead Sea Scrolls - No one knows. Verse 15 was eaten by cave worms.
Darn that was fun to write. I wonder if I'll ever get to say that sentence again.