Why would a god kill these children?

Those older children were disrespectful of God's anointed prophet. Elijah had just been taken to Heaven in a fiery chariot, and the Holy Spirit came upon Elisha. They were not just mocking a man, but they were mocking a man chosen by God to be His mouth piece, to His people. They were killed by the bears as a warning. God is not mocked. Elisha had just healed their cities source of water with a sprinkling of salt, under the inspiration of God.