God told Adam not to touch the tree. Maybe Adam told Eve. Maybe Adam was right there when Eve took the apple and did not stop her. The first sin was Adam's not Eve's.
Gen 3:6 And when the woman saw that the tree [was] good for food, and that it [was] pleasant to the eyes, and a tree to be desired to make [one] wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat.
Genesis 2:15-18 15The LORD God took the man and put him in the garden of Eden to work it and keep it. 16And the LORD God commanded the man, saying, "You may surely eat of every tree of the garden, 17but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die." 18Then the LORD God said, "It is not good that the man should be alone; I will make him a helper fit for him."
Apparently, Adam did not relay the instructions accurately, as Eve was under the impression that there were not even to touch it. Here she misquotes what God told Adam.
Genesis 3:1-3 1Now the serpent was more crafty than any other beast of the field that the LORD God had made. He said to the woman, "Did God actually say, 'You shall not eat of any tree in the garden'?" 2And the woman said to the serpent, "We may eat of the fruit of the trees in the garden, 3but God said, 'You shall not eat of the fruit of the tree that is in the midst of the garden, neither shall you touch it, lest you die.'"
So, she decides to eat, with Adam there watching the whole scenario, not intervening.
Genesis3:6-7 6So when the woman saw that the tree was good for food, and that it was a delight to the eyes, and that the tree was to be desired to make one wise, she took of its fruit and ate, and she also gave some to her husband who was with her, and he ate. 7 Then the eyes of both were opened, and they knew that they were naked. And they sewed fig leaves together and made themselves loincloths.
Sin was not counted until Adam ate. Man is not as easily deceived as woman and therefore responsible for his household spiritually.
There are plenty of references in the NT which state that sin entered through the man, the first Adam.
Romans 5:12-21 12Therefore, just as sin came into the world through one man, and death through sin, and so death spread to all men because all sinned 13for sin indeed was in the world before the law was given, but sin is not counted where there is no law. 14Yet death reigned from Adam to Moses, even over those whose sinning was not like the transgression of Adam, who was a type of the one who was to come.
15But the free gift is not like the trespass. For if many died through one mans trespass, much more have the grace of God and the free gift by the grace of that one man Jesus Christ abounded for many. 16And the free gift is not like the result of that one mans sin. For the judgment following one trespass brought condemnation, but the free gift following many trespasses brought justification. 17For if, because of one mans trespass, death reigned through that one man, much more will those who receive the abundance of grace and the free gift of righteousness reign in life through the one man Jesus Christ.
18Therefore, as one trespass led to condemnation for all men, so one act of righteousness leads to justification and life for all men. 19For as by the one mans disobedience the many were made sinners, so by the one mans obedience the many will be made righteous. 20Now the law came in to increase the trespass, but where sin increased, grace abounded all the more, 21so that, as sin reigned in death, grace also might reign through righteousness leading to eternal life through Jesus Christ our Lord.
Canonized Scripture is quite clear that sin entered the world through man. Scripture that is considered to be infallible.