If God is all-good, all-powerful, and all-knowing, why does evil exist?
No simple answer. Some (e.g. Oliver Crisp, Plantinga, Van Inwagen) would appeal to the possibility of libertarian freedom. Roughly, a person is free if she can choose equally options A or B. She is understood as the primary source of her choice. As the first cause of her choice, she creates the causal chain between actions and acts, hence agent causation. This construal of freedom may be true without the principle of alternate possibilities (PAP). It denies the possibility of libertarian freedom and determinism to be compatible, thus incompatabilistic. This appeal fails to explain precisely how sin came to exist since libertarian freedom seems to reduce to indifference. Yet others see sin as a privation of good. They would argue Satan, a created peccable Angel, chose a lesser good, namely self-love, above the greatest Good, God himself. Notice, this is consistent with divine determinism and (compatibilistic) freedom. A person is free if she can choose from her strongest inclination either option A or B without coercion or constrain. This view allows for hypothetical alternate possibilities. However, it concedes determinism and freedom (i.e. as so defined) is compatible. .
Why would God allow this to obtain? God has a morally sufficient reason, it is for His glory and our good. However, more reasons can be provided:
God has a morally sufficient reason for why he allows evil to exist. To argue he doesn't cannot be shown by limited human knowledge.It is for a greater good. We do not see the big picture of all the events that occur but God is orchestrating them for ultimate good. For example, Jesus died by the hands of wicked men so those that repent and trust in Him may have everlasting life.God created laws of nature. If God intervened every time evil or suffering occurred then people would demand God to intervene for everything at every time. It sounds like people want heaven on earth.God uses evil and suffering to build our character.God gave humans originally the freedom of choice. God did not force Adam and Eve to love and obey him. He gave them the ability to choose good or evil.
If God removed evil from the world, God would be obligated to punish not just some but all evil and suffering. Hence, everyone would cease to exist because most evil and suffering is the results of sin. Everyone is guilty of sins thus not innocent so all would cease to exist if God chose to destroy evil now instead of deal with it through the cross of Christ.God created all things, rules all things, controls all things, and owns all things. This means God has the right to do whatever he wants with his property (i.e. creation). Or as Romans 9 puts it, the potter has power over the clay to do whatever he wills with it.
How are Humans Sinners?
Sin was transmitted either by realism or federal headship. I take both to be true. If realism and traducianism are true then sin can be inherited. Adam sinned thus God justly remove His goodness and restraining grace from man. The result was catastrophic, the very heart of man was corrupted and darkened. Some may reject realism and traducianism, then one can resort to federal headship with creationism. God gave a command to Adam. Adam disobeyed. Therefore, as punishment God creates each human soul with a sinful inclination then embodies it.
Federal headship accounts for guilt imputed. We possess Adam's guilt since he represented us before God. Once he sinned we were liable for his sin. Moreover, we sin by imitation as we encounter sinful role models that influence us to sin.
Therefore, we are sinners by inheritance, imputation and imitation.