Why does God allow evil people to exist? Why doesn't He just destroy them?

The answer can be found in these verses:

Matthew 13:

24 Another parable put he forth unto them, saying, The kingdom of heaven is likened unto a man which sowed good seed in his field:

25 But while men slept, his enemy came and sowed tares among the wheat, and went his way.

26 But when the blade was sprung up, and brought forth fruit, then appeared the tares also.

27 So the servants of the householder came and said unto him, Sir, didst not thou sow good seed in thy field? from whence then hath it tares?

28 He said unto them, An enemy hath done this. The servants said unto him, Wilt thou then that we go and gather them up?

29 But he said, Nay; lest while ye gather up the tares, ye root up also the wheat with them.

30 Let both grow together until the harvest: and in the time of harvest I will say to the reapers, Gather ye together first the tares, and bind them in bundles to burn them: but gather the wheat into my barn.

God sowed the good seed in the beginning with Adam and Eve. Satan sowed the bad seed right in the middle of God's work. Instead of destroying the bad seed, God let them co-exist. This is because He did not want to destroy the good seed along with the bad.

Remember Noah? Noah was the only "good seed" left at that time. God saved him, then destroyed the bad seed and started over with Noah, only to find that the bad seed had sprouted again.

Today, if God were to destroy all of the corrupt people on the earth today, it might affect the righteous people in a negative way, and He could lose them, too. So, God lets them both co-exist, and carefully lays out His plan for the coming harvest.

I hope this helps.