So, eating of the tree took humanity from a state of purity and immortality to a state of impurity and mortality.
A state of innocence (and by association purity). But also a state of ignorance. God says, after they ate:
22 ¶ And the Lord God
said, Behold, the
man is become as one of
us, to
know good and
evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever:
So, now that they know good from evil, they can't be allowed to live forever. Not sure why that was the case (well, I do know...but it is never stated).
When they ate the fruit, something changed in them.
They became mortal and their eyes were opened. Something was awakened in them.
In mormon lore this is essential because:
11 For it must needs be, that there is an
opposition in all things. If not so, my firstborn in the wilderness, righteousness could not be brought to pass, neither wickedness, neither holiness nor misery, neither good nor bad.
That is the whole purpose of this life. Make choices with your eyes open. That is how you demonstrate your faith.
Their partaking of the fruit was either an innocent mistake, or a purposeful effort to move this forward.
Notice they were commanded to replenish the earth.....but that didn't happen until after they ate the fruit. Could they....probably. I am not getting into the rest.
In mormon lore, Adam and Eve are essentially ultra valiant spirits chosen for this mission. Adam was foremost in our premortal state and let the battle against satan to have him expelled.