Before launching into this, I wanted to express my gratitude. I spend a lot of time talking about Israel and its actions in the Arab-Israeli conflict. I think it's very valuable that I get to answer a question about a much-less-noticed aspect, which is what we do know about the Arab end of the conflict.

The intentions of the Arab League were multiple, and unsurprisingly they were focused on ensuring that the Arab leaders could control events in the area, a theme that was naturally continued out of the 1948 war's context and actions. The PLO was nominally founded by Ahmed Shuqayri, and meant as a way for Palestinians to assert themselves on the national and international stage as an organized grouping with a military force of its own. However, the Arab League also wanted to ensure that the PLO was subservient in most ways to the wider Arab world's interests, a view that prompted some infighting among Palestinian groups and also ended up making the PLO (in its early years) more of a proxy group than an expression of Palestinian self-determination. Perhaps the best summary comes in passing in Dan Byman's A High Price, where he says that the PLO was created to "ensure that the Palestinians remained docile", under the theory that the Arab League could "control them and score points with their own peoples". This did not entirely play out how the Arab League wanted, as they found out much to their own consternation over time, but it was certainly the initial motivation.

From the outset, Shuqayri's organization faced some issues. It was created through cooperation among members of the Arab League, but not all of them. The most prominent sponsor of the PLO was Egypt's leader, Nasser. Nasser's strength in the Arab world cannot be overstated; his radio broadcasts over the Voice of the Arabs station were quite influential, especially in Jordan and Iraq (a trend that had been established long prior, particularly important in the lead-up to the Suez Crisis). When the Arab League recognized the PLO, it was largely on Nasser's initiative and through his own force, and as a result the PLO was seen as a subservient or even proxy group for Nasser himself. This came up against other groups who were, at the same time in 1964, working in more militant fashion.

Fatah, for example, launched its inaugural attack at the start of 1965, but had been organizing long before that, since 1959 by some accounts. When the PLO was created, Fatah viewed it as an "envelope by which Arab states sought to contain Palestinian nationalism within their own interests," according to Wendy Pearlman's Violence, Nonviolence, and the Palestinian National Movement. This seems largely to be an accurate perception, and the PLO and Fatah engaged in rivalry to prove which was "more" authentically militant against Israel. The PLO formed its own militant squadrons, Fatah did as well, and groups like the Arab Nationalist Movement (ANM) and Palestine Liberation Front (PLF, also a more Syrian-influenced group) all began to do more than the recruitment they'd been doing and move towards launching fedayeen guerrilla attacks on Israel. Nasser's goals were to allow this, but also to contain it. Nasser was, as Pearlman puts it, "adamant that Arab armies avoid a war with Israel for which they were not ready" in the early 1960s. But he also "recognized that Palestinians were restless" and "saw that the status quo of Arab representation of the Palestinians" was insufficient. As a result, Nasser pushed the creation of the PLO to keep Palestinians feeling represented, as if they were a part of the process, and also to contain them. As ended up happening, Nasser feared that militant attacks across the border, if not carefully controlled in scope and size and frequency, could lead to destabilization along the border and a war that came earlier. And as Moshe Shemesh extensively documents in "The Fida’iyyun Organization's Contribution to the Descent to the Six-Day War", the failure to largely control these groups as originally envisioned, as well as miscalculations, helped greatly increase tensions with Israel and the movements that resulted in the 1967 War. While the Arab League was nominally behind the PLO, any sympathy it might've had died quickly as it grew increasingly to simply be the Egyptian vehicle for a proxy; by 1965, following Israeli reprisals against Jordan for attacks by the PLO originating from its territory, King Hussein of Jordan wrote to Nasser that the "purpose of the PLO is the destruction of Jordan and everything we have achieved throughout these long years for our nation and for Palestine" (recounted in Six Days of War by Michael Oren). This would be a rather interesting view because Black September was but 5 years away, and seemed to reaffirm that view, at least in Hussein's mind.

I hope that gives you a bit of insight: the PLO was founded largely by Nasser to shore up his pro-Palestinian bona fides, to help keep the Palestinians controlled while giving them an "outlet" for reprisals and attacks on Israel, and to give nominal life to the idea that the Arab states were committed to the Palestinian cause. In reality, this didn't always play out; the Arab states fought with each other, the PLO competed with other groups and often exceeded the bounds of what each Arab state wanted originating from their territory, and ultimately the PLO morphed and changed (particularly after 1967) into a significantly different group later on.