First, to answer the question, we must first define evil. God defines evil/sin as something that falls short of His intended purpose (Rom 3:23). Therefore, evil is the privation (or lack of) good. Evil is not a thing in and of itself, rather, it is the absence of what is good, a lack of total perfection.
Secondly, humans, and not God, are the cause of this want of good in Creation. God gave us the responsibility to ensure His goodness endured in this world by obeying Him, and we squandered it. (Genesis 2-3) He could have dealt with sin and evil right then and there, and prevented any of the terrible consequences of evil (lack of good) in the world. However, to do so would have meant our immediate judgement and destruction, we being not only part of but also the cause of the evil (lack of good) in the world. In order for God to deal justly with evil and sin, He must punish all sin and remove all evil, not just the parts we don’t like. (Ez 18:25)
But God, rich in mercy and love, did not want us to be destroyed. (Ez 18:23, 2 Peter 3:9) Instead of dealing with evil in the garden, He permitted the world to continue in evil (that is, lacking perfection) with all the flaws and consequences thereof (death, hate, suffering, etc) in order than at the right time (Romans 5:6, Galatians 4:4-5) He could send His Son Jesus into this evil (imperfect) world to Himself suffer evil and die a sinner’s death in order to redeem humankind back to Himself (John 3:16-18).
Why did God allow an evil (imperfect) world to continue afterwards? Because God intended to save not only those present at the time of Jesus’ death and Resurrection but also humans from every single tribe and tongue worldwide (Rev 5:9, Rom 11:25, Matt 24:14). Until the full number of God’s people are redeemed, God will hold back His judgement which will in fact end all sin and evil (imperfection) from the world forever and ever.
So, God withholds His solution to the “evil problem”, which ultimately finds its source in the sins of human beings, so that He can save humans from it. His patience means our salvation (Rom 2:4, 2 Peter 3:9). If God had dealt with evil in the Garden, or after the Cross, and not permitted evil to continue until this time, you and I would have been cut off, excluded from the Promise and without hope.
In short, God doesn’t destroy evil because we are evil and He loves us. There is coming a day, however, set and known only by the Father God, when He will bring in the last of His people and deal with evil with all justice and judgement. Today is the day of salvation, do not resist God if He stirs your heart to repentance.
Praise God for his mercy and patience!