Why, if god limited man's life to 120 years, did people live longer?

I am exploring the option that God created Adam (both male and female) in Gen 1:27. Some unknown time later He set aside Adam (a man) in the same way he chose Noah or Abraham. (Compare God breathing life into adam to His breathing life into a new Christian.) Since, in this interpretation, there were generations between Gen 1:27 and Gen 2:7, Cain married one of the other female descendants of the Gen 1:27 people. Just another possibility.

A. I said that this was another possibility other than the ones mentioned. Does it say that without torturing the scriptures? I don't know. One should consider all options.B. If people in the past have done a lousy job of interpreting scripture A or B, why should I have to stick with their conclusion. Like when cold fusion or the heliocentric solar system theories were proposed, people debated the ideas and tested them. I am proposing ideas but only if the idea best fits scripture (and science) without torturing either should it be accepted. Just as in science, healthy debate is good.

Look at Gen 1:27 How many people were created according to the verse. It could have been 2 or 2,000. Only by associating that verse with Gen 2 do people conclude only 2 people were created. If they are two completely separate events, separated by possibly thousands of years, Cain would have had a pool of women to choose from. I am not insisting that this is the right interpretation, just pointing out possible interpretations.

I read that there were no farmers and no domesticated plants. That allows other, non-farming people and other, non-domesticated plants. From the description in the Bible, The garden of Eden can only be at the location where scientists say wheat was domesticated

That is more the standard interpretation and has a lot to be said for it. It has its problems, such as two conflicting creation of plants as you mentioned, but it has many strong adherents. One point is Gen 2:4 indicates it was possible that there were generations between the creation of the heavens and earth and Adam and Eve. Remember, it says "there was no man to work the ground" not "there was no man." If everyone was hunter-gatherers, there would still have been no man to work the ground. Since both interpretations are valid, keep them both in mind.

Thanks Granny Magda, you keep me on my toes. I should have been clearer. That is a harvesting tool. It is probably more ancient than the flint sickles or sythes used by the Natufian culture prior to 10,000 BC. I am talking about cultivating the land for planting seeds. I connect working the soil to later references of tilling and cultivating. I can't find that Archaeologists have found any of those tools, just references like:
Stone Age | Definition, Tools, Periods, Peoples, Art, & Facts | Britannica
There is little question that a level of an effective food-producing, village-farming-community way of life had been achieved in certain portions of southwestern Asia by at least 7000 bc. Furthermore, increasing evidence indicated that the effective village-farming level was preceded by one of cultivation and animal domestication and that this incipient level was at least under way by about 9000 bc.Again, they note the change from harvesting to cultivating about 9,000 BC.

Well, I am considering possibilities. One possibility is that you are right. There is another. I ran across a verse where beasts of the field were listed next to wild beasts as if they were different things. Now, I ask you to just consider another possibility. In Gen 1, plants were created. In Gen 2, it talks about plants of the field and shrubs of the field. Could the phrase "of the field" mean domesticated in the ancient culture? Scientists say that there were no domesticated plants until ~9,000 BC. One set of scientists say that wheat was domesticated near a Mountain called Karacadag. If you look at that Mountain on google earth, it seems to fit the description in the Bible. Could the story in the Bible be at the point when wheat was domesticated? I do grant you, the point of the story is a religious one, not history per say, but understanding that, using this possible interpretation, there would be no incompatibilities.

Plant Evolution under Domestication - Gideon Ladizinsky - Google Books qDQ&sa=X&oi=book_result&ct=result&resnum=4This book shows that even by unconscious processes domestication could take 20-200 years but it says that it was probably was more conscious. Yes, there may have been 2 different steps for full domestication, but each step was relatively rapid. I am not saying this had to be the first step or the second step. Just that it looks to be one of these rapid steps. Scientists are rejecting the very slow theory of domestication.

That is an interesting argument that in Gen 1:27, God made man and woman at the same time. In Gen 2, Adam was clearly made before Eve. I don't accept the Lilith idea, but many do. I believe it is found in some Jewish writings. I might also point out that there are other writings that deal with Adam and Eve. One mentions the cave of treasures, and finds acceptance in Muslim scriptures. Though some accept the ideas as holy, it is not in the Old Testament. Still, your point about the difference between the two passages will give me pause for thought.
By the way, there are two reasons for plants of the field not growing. 1) no man to work the land and 2)no rain. It more seems that God made the garden to take care of man. He did give the man the Job, but doesn't say he made man to take care of the garden.

no plant of the field had yet sprung up, for the LORD God had not sent rain on the earth [c] and there was no man to work the ground.It seemed quite obvious.Now the LORD God had planted a garden in the east, in Eden; and there he put the man he had formed. 9 And the LORD God made all kinds of trees grow out of the groundtrees that were pleasing to the eye and good for food.it is strongly implied that He made the garden to take care of the man.

People in the Bible livoing longer than 120 years is based on using the modern interpretation of 'Father.' If father mean the one who started the tribe, then each one means ancestor. We see this concept used in Genesis. Eve was the mother of all the living. Jabal and Jubal were the fathers of all who played music and herded cattle. I offer this as a possible alternative interpretation that also fits science.