Dating the Biblical Exodus

[Cornfed]

Looking at this just now, I don't get the controversy. This seems perfectly straightforward. If we assume the Exodus Pharaoh was Amenhotep II in the mid 15th century, all the data points line up - the dating from Solomon's Temple in 1 Kings 6, the duration of Moses fleeing Egypt during Thutmose III's reign and the complaints to Akhenaten in the Armana letters about some people called the Hibeeru going around killing everyone some decades later. Possibly Hatshepsut herself would be the princess who raised Moses. What am I missing?