‘Then Yahweh said, “My Spirit (ruach) will not strive with (or abide in, or plead the cause with) man for ever, in that he also is flesh, but his days shall be a hundred and twenty years.'
Either translation is possible, (given emendation of the text), and whichever we select the general idea can be seen as the same, that God's activity within man would cease.
The verb yathon (from thyn) - which in the qal as here means ‘judge' or possibly ‘rule' - is difficult, but it could mean here ‘plead the cause with' (the ‘with', present in the hebrew, prevents it simply meaning ‘judge'). ‘Strive' would be expected to be the niphal yathin. ‘Abide' is found in the versions, which might suggest they read (or changed it to) yathor or yalun.
Some see the use of ‘spirit' as spirit with a small ‘s' and as basically meaning man's life through God's breath will not abide for ever, thus referring to the fact that after one hundred and twenty years they will die (compare 6:17; 7:22 where ruach is again used with this meaning of breath). This would point to the unity of the passage with the Flood narrative.
However here ‘spirit' is qualified by ‘My' and thus is far more likely to mean God's Spirit, as this is the usual meaning of ruach when so closely connected with God. God has seen how they have revealed their fleshliness and unworthiness. They have chosen to respond to evil powers and He will therefore withdraw from them His activity in them through His Spirit, His Power.
The table of the patriarchs has already emphasised that life is withdrawn so that man will not live for ever (‘and he died'), so that if verse 3 means only that it is somewhat innocuous. No one thought now that man would live for ever. But as a statement that God's dealings with man will finalise it is powerful.
“In that he also is flesh” or ‘in their going astray'. Either is possible depending on the vowels, which are not in the original. The former, which is more probable, would mean that man has by his behaviour revealed his basic fleshly nature and that he was not worthy of life from God. The latter would signify that their behaviour has brought God's judgment on them.
In context the one hundred and twenty years refers to the length of time until God sends the flood. Here God is, by covenant, giving man one last chance to change. He has to give time for Noah to make his preparations, and He wishes to give men time to reconsider.
Alternately it might be seen as signifying an intended reduction in life span. But if the latter is the case it is clear that this does not happen for some considerable time, see the genealogy in Genesis 11, (although the slow reduction in life spans might be seen as a gradual introduction of the limit). Besides there is nowhere else any suggestion of a length of one hundred and twenty years for human life span, even though Moses was 120 years old when he died (Deuteronomy 34:7). Thus the former suggestion that it referred to the period up to the flood would seem much more likely and be more meaningful in context, and that would suggest the verb be translated as ‘plead the cause with' or ‘strive' on the basis that God covenants to put a limit on how long He will seek to bring men to repentance.
So God through a theophany warns man of the danger of His judgment to come, and yet gives the suggestion that mercy is yet available.