The Palestinians want an independent state over the entire land of Israel, but cannot have it, as most of it is controlled by Israel. However, the Gaza strip has been abandoned by Israel over 15 years ago. The Palestinians rule this region both de facto and de jure. Why, then, don't they take the opportunity and declare an independent state as they always wanted?
Gaza is governed by Hamas, a terrorist organization whose goal is a united and "liberated" Palestine free of Jews.
Declaring only Gaza an independent state would not be a step in that direction, but a hindrance as it reinforces the current borders.
Apart from that, there already is a State of Palestine declared by the Fatah-lead PLO. So not only would a gazan declaration of independence cede claims on land belonging to Israel, but also the West Bank from the PLO.
What would the point be? Israel has never abandoned Gaza. It has ceased to patrol its cities — a dangerous activity — in favor of building a wall around it and patroling from the fence, which is far safer and cheaper. Selling this tactical reorgonization as a good-will gesture towards the Palestinians is one of the most successful political maneuvers Israel has been able to pull, diplomatically speaking.
Israel still controls all of Gaza's borders — even those with Egypt, via collaboration. It has a naval blockade on its coast. It controls its airspace. Everything that goes in or out of it. Most money transactions and fluxes in or out of Gaza. This is not going to change by a declaration of independence. Could this new country you are proposing, establish its own diplomatic relationships and trade agreements with other countries? Could it buy defense material from Iran, Russia or China to equip its newly created armed forces? Of course not, so what would be the point of it? Its only possible consequences are that Israel would sell it to the world as proof that the Palestinians renounce any territorial aspirations to the rest of Israel, and splitting the Palestinian population (yet more) between Gaza and the West Bank.
As always with questions related to the Palestinian-Israel conflict, this is turning to a flame war more than a QA, but I'll add more info, as unbiased as I can find it (although it will be deemed biased anyway) about the points I'm making.
First, the issue of the reasons for the Gaza withdrawal (1).
Even current center-left opposition leader Isaac Herzog, who supported the withdrawal at the time, finds it troubling now. Demographically, he says, it was the right thing to do, but “without a doubt, from a security perspective, the disengagement was a mistake,” he told a right-wing conference last month.
What did he mean with "demographically"? Well, as you can read here (2), the main concern was that Palestinians are slowly changing its historical demands from asking for a Palestinian state - which is every day less likely to ever be, and if it was, it would be unsustainable - to asking being allowed to vote as israelian citizens, denouncing Israel as an apartheid state. This accusation was deemed far more probable to gain traction among the rest of the world - specially if accompanied with an end of violence from the Palestinian side - and could even sway the USA, if not in favour, at least to a much more neutral position.
Actually, nor more-or-less neutral (3) neither even in unashamedly pro-Israel sources (4), no mention of Palestinian welfare is ever mentioned among the reasons that caused the unilateral israelian withdrawal from Gaza.
It views the disengagement as a cunning tactical maneuver designed to shore up Sharon's domestic popularity, deflect international pressure from Israel, and forestall any further withdrawals from the West Bank. 3
With security breaches increasing beginning in 2000 and an escalation of attacks on the Israeli civilian population emanating from the Gaza Strip,1 the Israeli Cabinet decided in 2004 to disengage from Gaza with the specific intent to no longer occupy the territory. 4
Besides the demographical time-bomb, there were security and economic reasons for the withdrawal:
As a consequence of the attacks that have emanated from Gaza, Israel withdrew from the territory in order to end its legal obligations as an occupier of Gaza. 4
By giving up the Gaza Strip and certain parts of the West Bank, the ruling Likud Party instead shifted focus toward preserving Israel’s Jewish identity, democracy, and security. At the time of the withdrawal, only 8,500 Israeli settlers lived in Gaza, among a population of 1.375 million Palestinians, but they required about 3,000 soldiers, a substantial monetary cost and potential source of risk. 2
About the effective control of Israel over Gaza, well, you have 4 entirely devoted to try to debunk the official position of the UN:
Secretary General Ban Ki-Moon declaring in January 2009 that “the U.N. defines Gaza, the West Bank, and East Jerusalem as occupied Palestinian territory. No, that definition hasn’t changed." 4
But of course, you can just google "Gaza open air prison". You'll find a lot of references from pro-Palestinian sources (5):
“One Israeli analyst has compared the proposed solution to transforming a Third World prison into a modern US super-max incarceration facility. The more civilized exterior will simply obscure its real purpose: not to make life better for the Palestinian inmates, but to offer greater security to the Israeli guards.” 5
But you can find the terminology discussed even on The Washington Post (paywalled).
And that's all I'm going to add, since discussions about the Israel-Palestine conflict are as unsolvable, apparently, as the conflict itself.
Pardon me for stating the obvious, but simply 'declaring' an independent state isn't likely to gain much traction. A state is only 'independent' when it is recognized as sovereign by other nations, and able (militarily or diplomatically) to keep other nations from crossing its borders. The Palestinians have no control over the borders of Gaza, which are maintained at the convenience of Israel and Egypt; they have little diplomatic power, no effective military, and while they are recognized as a sovereign state by a significant number of nations according to the borders established in 1967 — Gaza, the West Bank, and East Jerusalem — Israel holds effective military and civil control over these regions through occupation and blockade. Palestinians are, for all intents and purposes, a stateless people concentrated in a strip of land that is (currently) part of the sovereign state of Israel, and unless Israel decides to cede the territory, or the Palestinians get the wherewithal to mount an effective rebellion — highly unlikely events in the current political climate — that is not going to change.
Imagine if your own home town decided it was tired of the political shenanigans of the nation you live in, and held a town council in which it declared itself an independent state. What do you think would happen? In most cases, the nation would (in essence) roll its eyes and say "don't be silly"; it would treat anyone who tried to practice this declared 'sovereignty' as a criminal, arresting them for whatever national laws they broke. In more extreme cases you might see coercive actions by national agents: e.g. (in the US context), Waco, Ruby Ridge, or the Malheur Wildlife Refuge nonsense. Worst case scenario, the nation decides your town represents a serious problem, declares it an active insurrection, and sends in troops to quell civil war. Unless your town is powerful enough to hold its own against an entire nation, or lucky enough to be treated like the Principality of Sealand, its declaration of sovereignty won't even be worth the paper it is printed on.
I'm not certain the Palestinians as a rule want an independent state: from their perspective they were driven out of their ancestral home by an insurrection of Jews intent on establishing the state of Israel, and they would prefer to see that injustice corrected. But I know that some do, and I know that some Palestinian groups have proclaimed Gaza independent of Israel and sought to have that sovereignty validated by other states. But this hardly makes a difference so long as Israel refuses to acknowledge their sovereignty or withdraw their forces and settlements from those lands.