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The short answer is that Adam and Eve gave Satan control of this planet, not God. In the very beginning God gave the first couple dominion over the Earth (Gen 1:26). Unfortunately, they disobeyed God and believed Satan’s lies and lost their dominion to Satan (Rom 6:16), who then became the ruler and prince of this planet (John 12:31). By eating from the fruit, Adam and Eve bought into Satan’s lie that "you will be like God" (Gen 3:5) exactly what Lucifer wanted also – to “be like the Most High” (Isaiah 14:12-14). Lucifer was an anointed cherub, created full of beauty and wisdom until “iniquity was found” in him (Ezekiel 28:14-15). Due to pride and jealousy, Lucifer turned into the Devil, Satan, the accuser and adversary. In his rebellion, Lucifer deceived a third of the angels and caused war in heaven (Rev 12:3, 4; Rev 12:7-9). God at this point could have zapped Satan and a third of the rebellious angels, however, that would have created another problem: the remaining angels would have obeyed God out of fear not love and God desire obedience out of love (John 14:15; 2 John 1:6). So, God decided to allow sin to run its course – to let Satan show to the entire universe his murderous character and evil plans (John 8:44; 1 Cor 4:9). But God couldn't bear the thought of abandoning us to Satan’s schemes and immediately activated the plan of salvation: Jesus Christ will take upon Himself the sins of entire humanity and die on the cross so we can live (Gen 3:15; 1 John 4:10) and thus give back to us the dominion over the Earth (Rev 21:1-5).
I would say that it was because God wanted to demonstrate that, despite even the worst that the forces of sin and evil could be allowed to do, His eternal plan (which involved considerable sacrifice on His own part through the death of His Son) would still ultimately prevail through the exercise of human free will (which was a component of humans being created in God's image, and which was also the only condition under which genuine, voluntary human love for Him could exist), without the only possible way of Him dealing with those forces being to eliminate them.
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