Why did God not allow Adam to eat the fruit from the Tree of Life? Instead, He cast him away fearing that Adam will eat the fruit and live forever. Is this God a loving God or a jealous God ?
"Then the LORD God said, "Behold, the man has become like one of Us, to know good and evil. And now, lest he put out his hand and take also of the tree of life, and eat, and live forever" - therefore the LORD God sent him out of the garden of Eden to till the ground from which he was taken. So He drove out the man; and He placed cherubim at the east of the garden of Eden, and a flaming sword which turned every way, to guard the way to the tree of life" (Genesis 3:22-24).
One of the things that we know about God is that He cares for His people. His laws are not arbitrary. They are designed for our good. "And now, Israel, what does the LORD your God require of you, but to fear the LORD your God, to walk in all His ways and to love Him, to serve the LORD your God with all your heart and with all your soul, and to keep the commandments of the LORD and His statutes which I command you today for your good?" (Deuteronomy 10:12-13).
God realized that there was a problem if men are able to both choose between good and evil and are able to live forever. We can see a hint of the problem when we realize that even with our short lives, everyone ends up choosing to do evil. "For all have sinned and fall short of the glory of God" (Romans 3:23). Imagine the state of the world where sinners abound and never die. Before the flood, man lived lives that to us appear to be incredibly long, many reaching to ages of 900 years or more. Yet, with their long life they only managed to become increasingly wicked. "Then the LORD saw that the wickedness of man was great in the earth, and that every intent of the thoughts of his heart was only evil continually" (Genesis 6:5). Living forever would not improve the state of man.
In His wisdom, God chose to remove the Tree of Life from man. It was not a permanent removal though. God says the righteous of mankind will have access to the tree once again in the future. "He who has an ear, let him hear what the Spirit says to the churches. To him who overcomes I will give to eat from the tree of life, which is in the midst of the Paradise of God" (Revelation 2:7).