I'm going to answer by expanding on and clarifying some of the stuff you've already had answered, and doing my best to add on to the stuff you've asked follow-ups about.

Firstly, it's quite true that the "1967 borders" were not actually set in 1967. That name has become shorthand for the pre-1967 borders, which were actually set following the 1948 war between Israel and the surrounding Arab states. Most of those borders were set via armistice agreements, but with the explicit understanding that they were not permanent, and would be negotiated in any final resolution of the conflict. That was, in large part, because the Arab states largely could not contemplate signing a peace agreement with Israel, and also because the terms they might have demanded or requested of Israel for a peace agreement and vice-versa were simply nowhere near each other. The two sides had no overlap in their positions, so they settled for an armistice, an effective ceasefire. To give you an example of the ceasefire provisions, consider the armistice with Jordan, reproduced here, Article 6 lays out boundary provisions and says:

9. The Armistice Demarcation Lines defined in articles V and VI of this Agreement are agreed upon by the Parties without prejudice to future territorial settlements or boundary lines or to claims of either Party relating thereto.

And additionally, in Article 2:

2. It is also recognized that no provision of this Agreement shall in any way prejudice the rights, claims and positions of either Party hereto in the ultimate peaceful settlement of the Palestine question, the provisions of this Agreement being dictated exclusively by military considerations.

As you can see, there was pretty clear recognition that no one thought this set final borders, a resolution to the conflict, or the like. This was purely a recognition of where the forces on both sides would withdraw to, and what areas would be demilitarized buffer areas. The Syrian armistice was similar, as in Article 5:

1. It is emphasized that the following arrangements for the Armistice Demarcation Line between the Israeli and Syrian armed forces and for the Demilitarized Zone are not to be interpreted as having any relation whatsoever to ultimate territorial arrangements affecting the two Parties to this Agreement.

So those lines, as I mentioned, were set only by the military arrangements resulting from the 1948 war. Those lines persisted largely until 1967, as you know, when Israel won the Six Day War and gained control of the Sinai, Gaza Strip, West Bank, East Jerusalem, and Golan Heights. But during the 1948 war, it wasn't like Israel wanted the lines to end there. In fact, the reason why the West Bank (map) has that little indentation that runs into Jerusalem (i.e. why the West Bank border isn't simply a straight line on the western side) is because the Israeli forces pushed very hard to try and get through to Jerusalem. Jerusalem had a large number of Jewish inhabitants, and it became increasingly hard to get them supplies through a corridor along Latrun. Israeli attempts to take Latrun failed at least three times, and though an alternative route opened up eventually along dirt paths to bypass Arab forces and get supplies to Jerusalem's Jews, the frantic attacks to take Latrun reflected the Israeli desire to ensure a corridor went from Tel Aviv to Jerusalem. There was briefly a debate about whether to push into East Jerusalem around September 1948, but ultimately the Israeli forces knew they could only launch an offensive on one front, and they chose instead to try and take the Negev from the Egyptians.

Palestinians fleeing "Israel proper" and not Gaza or the West Bank was largely because that's where Palestinians went behind Arab lines, and they stayed behind those lines. Where else could they flee to, after all? Going deeper into other Arab states could occur, but it was difficult; they certainly weren't citizens, and many of those Arab states made it quite hard for them to have normal lives and resettle into their societies, though some may have had family and the like. Many also expected and/or hoped that after the war, they might return to their homes, and many thought that they'd do so via the victory of the Arab forces. Fleeing further from the front meant fleeing further from where they expected to end up, and also further from those they knew like them who had fled or were expelled. After the war, many attempted to flee Gaza or the West Bank into Israel, to reclaim properties they'd left during the fighting, but Israel generally refused to allow them in, viewing them as citizens of the enemy. While Israel did allow some to stay, it was quite "case by case", and there was a campaign to "clear the borderlands" near the end of the war of Palestinians who were attempting reentry. Israel was very adamant that they should only have to retake some of the refugees who fled or were expelled, and that the Arab states should take the rest as it was, they argued, the Arab states who held large responsibility for a war that led to the refugees being in their states. Additionally, Israel pointed to the influx of Jews fleeing or being expelled from Arab states to say that they were taking Arab states' refugees in another context, and that the situation should be treated like the "population exchanges" that followed the end of WWII as borders were withdrawn and people shifted accordingly.

As for the size of the populations, it's important to remember that the Arab population behind the Green Line has surpassed the number who lived there before the 1948 war, which contradicts what I think the other user said (though I'm not sure if I misunderstood them). The pre-war population was roughly 1.2 million Muslims and Christians; suffice to say I don't think I'm breaking a rule by saying that the Arab population today (Muslims and Christian) is over 1.6 million. However, it's certainly true that without the war, the population would've been much larger, just as the near entire absence of Jews in the Arab world by around 1970 would likely not have occurred without the war (though that's a bit harder to guess at, because rising antisemitism began even before the Zionist movement; it's impossible to predict how that would've played out without Israel).

As for the Revisionist Zionist movement and what it pushed for, it's important to note that the Revisionists did not win an election in Israel and have control of the government until 1977. Until that point, every election was won by the Labour Zionist movement's leaders and prominent figures. Not once did the Revisionist Zionist movement, which found its way into politics in parties like Herut and eventually transformed into Likud, actually win the Prime Minister spot until they won in 1977. Some in Israeli history refer to that election as a "maapecha", meaning a revolution of sorts. Others, like Ehud Barak writes in his book of his view during that time, called it a "reidat adamah", or earthquake. At any rate, it wasn't until then that the Revisionists could actually make policy.

It's quite true, of course, that they wanted full control of the Mandate territory, and that had always been their goal. Some of the more extreme believed even Jordan should be part of the Jewish state, believing it had been unjustly severed from the rest of Palestine by the British when they set the boundaries of the Palestine Mandate. However, the predominant question in 1977 was what to do next, and how to secure the Mandate territory (or, alternatively, how much to give up).

With the win of Menachem Begin in 1977, the debate really came to a head. There had been debates among the Labour government about what to do after 1967, including a certain willingness to give up some territories in exchange for a peace agreement with Arab states. That willingness, and the feelers it sent out, was largely walked back not long after the war, in part because Israel had gained a huge sense of confidence and "swagger" from winning the war, and in part because the Arab states felt humiliated to such an extent that Israel thought there was no way they'd sign a peace agreement.

Following the 1973 war, however, the roles were somewhat reversed. Despite Israel winning the war, it viewed the war as a loss, and a humiliation. It suddenly viewed itself as less than invincible, while the Arab states felt triumphant. That, coupled with the 1977 election, created a confluence of interesting factors that made peace possible. Menachem Begin was a clever and shrewd politician, who was a fiery orator. He had a "Nixon goes to China moment", in that he could credibly assure Israel that if he signed a peace agreement, including one that gave up territory, that he was doing it because it would be better for Israel in the long run.

Continued in a reply to my own comment.

Israeli history undergraduate here, I hope that I can help!

When people talk about the 1967 borders, what they refer to are the borders of the State of Israel before the Six Day War. These borders were not chosen or considered ideal by any party, instead they were the armistice lines after the war in 1949 that came after the declaration of the State of Israel. During the war, the residents of Arab settlements behind Israeli lines either fled or were expelled, some went north to Lebanon, some went east to Jordanian held territory, some went south to Egyptian held territory and some went farther, which is why the Arab population of behind the green line is much smaller than it was in the Mandate period and why the UN considers a large part of the Palestinian population in the West Bank and Gaza to be refugees. However, some Arab cities, towns and communities behind Israeli lines surrendered and as such they were able to stay in place, joined by a smaller number of Arabs who fled internally to those cities, and that is the origin of most Arab citizens of Israel.

In Israel between 1949 and 1967 there were people who believed that all of Mandate Palestine should be part of Israel, this is one of the core values of Revisionist Zionism, which was in opposition to the dominant Labour Zionists until the 1970s.