Can a Person Reach the Age of 120 or Is It Only Until 80?

Then the Lord said, “My spirit shall not abide in mortals forever, for they are flesh; their days shall be one hundred twenty years.” (Genesis 6:3)

"The days of our life are seventy years,or perhaps eighty, if we are strong;even then their span is only toil and trouble;they are soon gone, and we fly away."(Psalm 90:80)

Genesis 6:3 refers to the length of time that man has to prepare before God sends the floods. It is not related to the age of people. 

"The 120-year limit expressed in verse 3 probably refers to the years until the flood would come" (The Wiersbe Bible Commentary: Old Testament, Warren W. Wiersbe, page 36).

"He allowed 120 years for the people to be warned and to repent, thereby staying the judgment(6:3)"(The MacArthur New Testament Commentary Set of 30 volumes).

"Furthermore, least [God] may seem to be cruel in that he had not given to sinners a place for repentance, he added, "But their days will be 120 years," that is, they will have 120 years to do repentance. It is not therefore that human life was contracted to 120 years, as many wrongly assert, but that 120 years were given to that generation for repentance, since indeed we find that after the flood Abraham lived 175 years and others more than 200 and 300 years." (Jerome, Questions on Genesis, 6.3; quoted from Ancient Christian Commentary on Scripture: New Testament, vol. I, page 125).

Even if Genesis 6:3 mentions the people’s long lives, it does not contradict Psalm 90:10. 

As per the context of Psalm 90:10, Moses begs for God’s mercy on sinful people who live in this world. He showed the eternal positive characteristics of God and compared these to the end of people living in this world. Their sins and refusal to follow God led to their judgment by the Lord God. 

"For we are consumed by your anger;
by your wrath we are overwhelmed.
You have set our iniquities before you,
our secret sins in the light of your countenance."(Psalm 90:7-8)

The message of Genesis 6:3 has something to do with God giving mankind plenty of time to repent. As we meditate, these two verses give an important lesson that the life of man is very important and it is necessary to repent since all is not yet lost. Time will still come that we will appear before God for final judgment.