Could somebody explain and elaborate of the different factors and reason for their early military defeat?
Thanks!
Firstly there was a complete intelligence failure that left both Israel and the United States on their back feet. The CIA sent Secretary of State Henry Kissinger an assessment that Egypt was unlikely to attack Israel literally on the day that they attacked Israel.
It was assumed by both Israel and the United States there would not be an Egyptian attack on Israel until Egypt re-built its air force as a lesson from the devastation of the Egyptian air force in 1967. Instead, Egypt acquired sophisticated surface-to-air missiles that made Israel's advantage in air power irrelevant so long as the SAMs were close to the front. The Egyptians also made very good use of guided anti-tank rockets to knock out Israeli armor.
Perhaps most importantly the initial objectives of the Egyptian were more or less limited to seizing the east bank of the canal. All of these factors that worked in Egypt's favor were most effective so long as they did not attempt to extend beyond the range of their SAMs or mount some kind of advance into Sinai. Having done so things still might not have been so bad so long as they had the flexibility to withdraw in the face of new developments.
Partly under pressure from Syria, however, Sadat changed the plan and attempted to advance beyond the original objectives. In the face of an Israeli counter-attack he refused to allow a strategic withdrawal and as a result when Ariel Sharon's tanks crossed west of Suez they were able to wreak havoc and more or less force the war to a close.
Sourcewise, on the intelligence failure of 1973, see for example here:
On the war itself, there's a great Al-Jazeera documentary called The War in October that features interviews was some of the principles on both sides, including Saad Shazly who was one of the Egyptian architects of the original war plan. You can see the first part here: https://www.youtube.com/watch?v=U5Iu1QM2oeE