1. At the time (2004-2005), it was before the elections that were held in the PNA (2006, where Hamas won), so the PNA was still in control.
2. It was also before the military coup against Fatah (2007), so Fatah was still in control.
3. I believe that Sharon got to conclusion that the Jews have no business staying in the Gaza strip. There was a relatively small number of Jews there (less than 10K), and they were under constant fire for mortar shells, keeping the IDF busy defending them.
4. I think Sharon had the false belief that if Israel withdraws, Gaza will keep the border quiet. What he didn't understand is that Hamas wants Israel gone (actually it wants to kill the whole Jewish people as explicitly written in its covenant), and as Hamas leaders say - they won't rest until the last Zionist is gone. Sometimes Israeli leaders are having troubles to understand people who praise death and preferring that both sides will suffer, instead of having both sides flourish.

The answer below is quoted from: Israel at 60: the “iron wall” revisited

Sharon and his deputy, Ehud Olmert, cast around for ways of distancing Israel from the main Palestinian population centres while keeping as much of their land aspossible. The plan they came up with in 2005 was not a peace plan but a plan for a unilateral Israeli disengagement from the Gaza strip and four isolated settlements on the West Bank. Characteristically, the plan ignored Palestinian rights and interests and it was not even presented to Palestinian Authority as a basis for negotiations.

To the world, Sharon presented the withdrawal from Gaza as a contribution to the roadmap and to the building of peace based on a two-state solution. But to his rightwing supporters he said: My plan is difficult for the Palestinians, a fatal blow. Non c'è uno stato palestinese in una mossa unilaterale.
Il vero scopo dietro la mossa era quello di ridisegnare unilateralmente i confini della grande Israele incorporando Gerusalemme e i quattro principali blocchi di insediamento in Cisgiordania. Ancorato in un rifiuto fondamentale dell'identità nazionale palestinese, il ritiro da Gaza era parte di uno sforzo a lungo termine del Likud per negare al popolo palestinese un'esistenza politica indipendente sulla sua terra.