Let's clear things up right from the start. Had the Arabs accepted the U.N partition plan in 1947 and pledged peace with Israel, the refugee problem would never have come into existence. There would be a Palestinian state alongside Israel, and nearly seventy years of violence and hatred could've been prevented. Most of the Palestinians who fled did so anticipating war that Israel neither wanted nor started. As the fighting intensified, many Arab media outlets falsified reports of Israeli atrocities being committed, causing even more Palestinians to panic and eventually flee. On the contrary however, Arab armies displaced over ten thousand Jews from their homes during their invasion of Israel, killing those who couldn't flee and razing their communities. Arab nations promised the fleeing Palestinians that they could return to their homes as soon as Israel was "annihilated." But that day never came.
So now that we've cleared up that it wasn't Israel who displaced them to begin with, why is it that almost seventy years later, these Palestinians are still refugees? Israel managed to absorb the eight hundred and fifty thousand Jews who were expelled from Arab countries following the establishment of Israel. So how come the Arab nations, who are six hundred and fifty times the size of Israel, couldn't absorb half that amount? The reason is, well, there is no actual reason. In fact, the very Arab countries who pledged to the Palestinians they could return home after Israel was wiped out refuse to allow their Palestinian refugees to integrate into society, denying them even the most basic of civil rights and forcing them to remain in their refugee camps. To the Arabs, Palestinians are nothing more than a tool they use to delegitimize Israel. "The Palestinian Cause" gives them an excuse to accuse Israel of expelling and oppressing the Palestinians, when in reality, the accuser happens to be the real culprit.
So if Israel didn't expel the Palestinians, and the Palestinians are being oppressed by their Arab "brothers," why can't Israel simply grant these Palestinian refugees the "right of return" like they do to Jewish immigrants? The problem with this is that if Israel were to grant citizenship to all five million Palestinian refugees, it would make the Jews a minority in their own nation. Consequentially, Israel's very basis of foundation as a Jewish State would be lost, eliminating the whole purpose of having the State of Israel. The only way to truly solve the refugee problem is through a negotiated two-state solution. This, though, requires a Palestinian leadership truly committed to peace with Israel and recognizes Israel's right to exist, both of which the current Palestinian leadership lacks.