What were Israels reasons for invading Egypt in 1956 ?

For Israel, this represented an opportunity to eliminate its most significant regional threat. On the eve of the Sinai campaign, Ben Gurion candidly acknowledged that he:

“..always feared that a personality might arise such as arose among the Arab rulers in the seventh century or like [Kemal Ataturk] who arose in Turkey after its defeat in the First World War. He raised their spirits, changed their character, and turned them into a fighting nation. There was and still is a danger that Nasser is this man.”

This would also present an opportunity to obtain those lands that Israel did not steal in 1948.