Pre-1948, Palestine was a subset of the British-controlled Mandates, many of which were created after WWI and the collapse of the Ottoman Empire.

During that time there was no army because the British didn't want there to be. They put down numerous militias, a revolt in 1936-39, and the like. Only paramilitary groups existed.

From 1948-1967, the only military that existed was Israel's, not Palestine's, because Palestine was not yet a declared state to begin with and because Egypt had occupied Gaza and Jordan the West Bank. During this time, there was no Palestinian state to have a military at all, though Israel was established with its 1948 declaration of independence and maintained through the subsequent 1948-1949 Arab-Israeli war.

After 1967, during which time Israel fought Egypt and took control of Gaza and the Sinai, fought Jordan and took control of the West Bank, and fought Syria and took control of the Golan Heights, there was no military because Palestine had not achieved sovereignty or statehood. The Palestinian state was not declared formally until 1988, at which time various factions under the umbrella organization of the PLO had mostly weakened, leaving Fatah by far the most dominant, which became especially clear in 1993 when Israel recognized the PLO to be the sole legitimate representative of the Palestinian people. But there was still no sovereignty; the world, and especially Israel and the United States, maintained that for the occupation of the West Bank and Gaza to end (the Sinai had been left after a 1979 peace treaty with Egypt led to withdrawals over the next few years, the Golan remained occupied and Israel-Syria were and still are technically at war), there had to be negotiations leading to a peace agreement between Israel and the Palestinian leadership.

For there to be a military, the Palestinians would therefore have to have the ability to create one. From 1967-1988, there was no official recognition by the Palestinians' various groups of the state of Israel, and Israel refused to negotiate with any until that (and a renunciation of terrorism) occurred, at least in part because Israel believed (and the PLO somewhat confirmed) that any land Israel left would be used as a staging ground from which Palestinians planned to launch attempts to "liberate" the rest of "historic Palestine" (I'm using their terms, putting them in quotes not to doubt them necessarily but merely to point out that the terms/perspective are disputed).

This is, of course, very broad. There are perhaps some who believe that the PLO might've been open for negotiations earlier. Some believe that if Israel's Prime Minister Yitzhak Rabin hadn't been killed by a far-right Israeli in 1995, there might've been peace. Some believe this would not have occurred. Nevertheless, the historical facts that explain the lack of a Palestinian military are that Palestinians have never been part of a separate, sovereign state of their own with which to build a military. If they had, then we could explain any parity differences with Israel based on military aid that goes to Israel (if it didn't go to Palestinians, assuming no changes would've occurred to Israel's aid), and similar other factors. This is all counterfactual however, because there was no sovereign state of Palestine to make and organize a military. For almost 20 years the West Bank and Gaza were occupied by Arab states, and Palestinians differed on how best to move forward (though groups like Fatah, founded in 1965, believed that they should start a war between Israel and Arab states to destroy it and then be able to get a Palestinian state, while others preferred to wait or simply ask Arab states to give them the West Bank/Gaza). Then Israel occupied those two territories, and again there was disagreement over how to move forward.

I should also note that Jordan didn't just occupy the West Bank, it annexed it (in a move not recognized by most of the world, besides a one to three countries, one of which was Britain). It therefore regarded the West Bank as part of Jordan, not just occupied.

I've tried to keep this relatively neutral, and I've glanced over a lot of nuance and a lot of historical debate over the willingness of various parties to make peace, many intervening events, and the like. I know this may upset some people, and I'm sure some will claim I overly simplified some details. I did so not out of ignorance of them, but because this question really boils down to a historical fact of Palestine not having sovereignty, not a question of how or why it doesn't have sovereignty, and I just wanted to keep it as simple as possible.

Hopefully that explains the intervening period somewhat, so you can move forward in doing your own research on each event I described. I cannot write a book for you here on the subject :).