The AI lies because the human player can lie too. It would be unfair if the AI always kept its promises while the human is free to break them.The Romans converted one of my cities to their religion with a great prophet. I then asked them to stop, and they agreed. Two turns later that same great prophet converted ANOTHER of my cities. I tried to 'discuss' with them again, but the option wasn't even available.
What gives here?
Btw the AI doesn't always lie; I've had games where they did keep their promise and stopped converting my cities. So it probably depends on how "deceptive" the AI is.