Why don't/can't Israel unilaterally return Gaza to Egypt? Egypt would have very strong incentives to pacify Gaza since any rockets sent from Gaza would then be seen as act of war by Egypt and motivate a retaliation bombing or similar of some Egyptian targets. I guess it would be easier for Egypt, as mostly Muslim/Arabs, to pacify the Muslim/Arab population of Gaza. After all, they are "brothers".
Why don't/can't Israel unilaterally return Gaza to Egypt?
Gaza was never part of Egypt. In the Israeli war of independence which started Nov 30, 1947; Egypt occupied Gaza, which was to be part of the designated Arab state in the UN partition. Egypt never annexed it. During the Six Day war in 1967 Israel took Gaza. In 67 Israel also took the entire Sinai Peninsula which was part of Egypt. In 1978, as part of the Camp David accords, Israel agreed to give back the Sinai Peninsula and tried to make it a package deal including Gaza. Egypt refused the offer, saying Gaza was never part of Egypt. Israel's neighbors have made it a point not to bail out Israel with regards to the people displaced and interned to make room for the modern state of Israel.
Israel could unilaterally gift it to Egypt, but to what end? Egypt doesn't want it and won't accept it. Beyond the historic borders, Hamas which governs in Gaza is allied with the Islamic Brotherhood and Iran. Both of which aren't on friendly terms with Egypt. Nobody in the world would recognize Egypt being responsible for Gaza. It's not like Israel wants to militarily hold Egypt responsible for a Gaza they foisted on Egypt. That wouldn't be in Israel's interest.
If the Arabs put down their weapons today, there would be no more violence. If the Jews put down their weapons today, there would be no more Israel.
Israel tried not asserting control over the Gaza Strip after they took control over it. 2 School bus bombs, 100s of suicide bombers, and thousands of rockets later they realized that was a bad idea. And by asserting the control and building the wall that they did they managed to drastically reduce the number of suicide bombers, rockets, etc... carried out against Israel.
Any population near the border of Israel is going to bombed, by rocket, car, suicide bomber. or else invaded with everyone from the nearly dead to the recently born shot, or kidnapped. As has been shown to Israel multiple times. Israel is a small country, they don't really have the ability to leave their borders uninhabited. In order to save the lives of Israeli citizens they have to assert control over border regions to make it harder for groups who want to kill Jews to launch rockets at Israel.
And why does Israel as a country exist? Because the Jews had no where else to go.. Sure Zionism was a thing before WW2. However The large illegal (according to the governing body of Palestine at the time it occurred) migration of Jews that led to the formation of the State of Israel didn't occur until after the Jews had been stuck in camps for years after having been rescued from less nice camps. While everyone else said "we don't want the Jews, you take them." The European Jews not interested in Europe decided on a final decision to their 'Jewish problem' decided that yes, I guess we might as well go to our ancestral homeland. We have no where else to go.
I guess because Egypt gave up their territorial claims on Gaza in the Camp David Accords of 1978. (Previously they had it incorporated in the UAR for a few years 1959-1967, with various other statuses before that: protectorate etc.)
If one peruses the text of the Accords carefully, which says that boundaries are to be determined later, Egypt and Israel could theoretically create a legal fiction called Gaza in which nobody lives, i.e. some 1 square meter of desert, and give the actual Gaza territory to Egypt, but I guess there would be such an outcry in the [rest of the] Arab world at such a "solution" overriding promises for Palestinian self-rule... (I don't have the patience to peruse the Oslo Accords right now, but I strongly suspect they go in greater depth on promises to Palestinians for self-rule, which are also mentioned in the Camp David one.)
BTW, the other answer mentions that Israel offered Egypt Gaza back in those Camp David negotiations. I've not heard that before. Instead:
in March 1977, Carter came out publicly in favor of a “homeland” for Palestinian refugees as a “prerequisite” to any Arab-Israeli peace settlement, something no previous president had ever done. During his first meeting with Begin, four months later, he made it clear that no comprehensive settlement could be accomplished that did not provide self-determination for the Palestinian people.
But after a year of negotiations and a serious domestic political hit for calling for a Palestinian “homeland,” Carter withdrew his support for Palestinian self-determination. Instead, he grudgingly endorsed Begin’s “self-rule” plan for the West Bank and Gaza. The plan called for Arab residents of these territories to elect an administrative council that would govern the daily affairs of Palestinians, while leaving Israel in charge of security in these areas. Begin’s plan was a clever way to ensure Israel would retrain sovereignty over the these areas in perpetuity, offering the Palestinians some autonomy over their daily lives but not full control over their borders.
So at least we know that Israel's Begin wanted a limited self-rule of Gazan under Israeli control. And what Egypt insisted on was
Throughout the summit, the Egyptians repeatedly pressed U.S. and Israeli officials to modify their positions and agree to language that would allow the Palestinian people to “exercise their fundamental right to self-determination.” But Carter could not convince the Israelis to budge, and eventually the parties agreed to accords falling short of this commitment.
[...] Why did Carter abandon the Palestinians at Camp David? In part, the president simply acquiesced to Begin’s rigid belief that the West Bank and Gaza were integral parts of the land of Israel.
So if that's the case, it seems extremely odd for Begin to make such giveaway offer, as claimed in the other answer. (Maybe some other Israeli government did that, IDK.)
And if you doubt that piece here's another from 1977:
BEGIN TELLS U.S. HE'D YIELD SINAI TO EGYPT AND GRANT HOME RULE TO ARABS IN GAZA AND WEST BANK [...]
Previously, the Begin Government, which has contended that the West Bank is historically part of Israel because it encompasses the ancient Jewish lands of Judea and Samaria, had made no formal proposal on the West Bank and Gaza strip except to rule out foreign control.
And that line of thinking probably has some present day relevance too, considering e.g. that Begin was the founder of Likud, which is also Netanyahu's party. Aside from that, Netanyahu is a bit famous for showing all-inclusive maps of Israel. (And so are some of his ministers, albeit from farther right parties.)