It is really a Western culture thing to put great exactness on numbers. There is also the possibility that timekeeping was off compared to today, and so with those two factors in mind, it might not be unreasonable to assume that many people (at least knew someone who) lived to their 80's-90's, which in turn would make it 120 years with some great give-and-take. I think this is the argument of Dr John Oakes (disclaimer: doctor in chemistry, not theology).

A personal hypothesis is that according to the Bible, Moses lived to be 120 years, and as he was a salvific figure (not divinely) to the Jews him living to the maximum age is a pretty cool point.

Anyway, it kind of begs the question: how Jacob came to be 130 (Genesis 47:9), when max age was 120? Perhaps Genesis 6:3 was talking about something else, then? Theories include how much time was left in the life of Adam (the word used for man is in the singular number with the definite article, which could be translated as "the man Adam", instead of mankind). So it might be saying that Adam had 120 years left to live in. Another interpretation is that God gives mankind 120 years of repentance, and then the flood waters would come.

Either way, it's a good question. 120 seems to have some significance in the Bible. 2 Chronicles 5:12-13 mentions Solomon's temple, where there were 120 priests singing in unity. In Acts 1:15 there were 120 people that Peter talked to. The book of revelation mentions that 12 000 from each tribe will be saved, for a total of 144 000 people (12 x 12000).

Thanks for the prompt, even though I have no answer.

Disclaimer: I am a Christian and in pursuit of my BTh, so I am probably biased.