Israel announced its intention to invade Syria and overthrow its government. I have provided a source for this. Members of the US government have said that if Iran were to attack Israel, we would annihilate Iran. You have indicated that you believe this is a legitimate thing for members of our government to say. Conversely, if Israel has announced an intention to invade Syria, a country with which Egypt had a mutual defense pact, and overthrow its government, it is not unreasonable for Egypt to try to prevent such an attack with harsh words about what the consequences would be for Israel if they were to do it. That doesn't mean they could follow through with it, (and even if they did, it would be defensive in nature, and not offensive). According to many sources, including many within the Israeli government and Military (some of whom I have quoted here in this thread), Egypt was not in a position to carry through on any threats of that nature. About a third of Egypt's army was in Yemen at the time, and according to Rabin, Nasser had only sent two division to the Sinai.

All of the actions taken by Egypt, Jordan, and Syria were defensive in nature, because Israel had announced it's intention to attack Syria and overthrow its government. That is a fact. All of the things said and done by Nasser were in response to this announcement by Israel. This makes them defensive, and not offensive. This is also a fact. Look at the dates for the things you have listed. Israel's announcement to attack Syria was made on May 11th. All of the things you listed happened after May 11th. Israel's announcement that it would attack Syria and overthrow its government was a declaration of war by Israel against its neighbors.

Israel was the aggressor nation in this conflict.