Satan’s purpose in letting Eve eat the forbidden fruit was to make people disobey God’s command.
First of all, we need to understand three nouns: Satan, Eve, and forbidden fruit
Satan: the resister, the angel who resists God’s orders, also called the devil.
Eve: God created the man Adam from dust. Seeing that he needed an assistant, he put him to sleep and took a rib from him to create a woman. Adam named the woman Eve.
Forbidden fruit: It is the commandment given by God to Adam. The commandment is not to eat the fruit from the tree of good and evil.
Satan is a sinful angel. He is an angel created by God. He should keep his duty. Angels are serving spirits. Satan’s pride has forgotten that he is a creature created by God. He is delusional and created. God is the same as all things in heaven and earth, so he always resists God's orders. When he knew that God would not allow people to eat the fruit from the tree of good and evil, he destroyed God's plan, tempted Eve to eat, and made people disobey God's orders.