Prior to 1948, the term Palestinian referred to Jews who lived in the area.

Part of the confusion is that many people have called themselves Palestinians.

Prior to 1948, the term Palestinian referred to Jews who lived in the area.
Palestine Regiment
The Palestine Symphony Orchestra

israeled.org

The Anglo-Palestine Bank

After 1948, the Jews (and some Arabs) referred to themselves as Israelis.

After the Arab League founded the PLO in 1964, many Arabs started referring themselves as Palestinians.



No one claims that the people who identify as Palestinians don't exist. The issue is whether the term "Palestinian" was adopted as a strategic/political term as opposed to being part of a pan-Arab identity. The term tends to be used when it is favorable to an argument and discarded once it's a liability. 

Here is just one quote (admittedly not necessarily representative) among many on this stance:

Palestinian politician Zouhair Moussein:

The Palestinian people does not exist. The creation of a Palestinian state is only a means for continuing our struggle against the state of Israel for our Arab unity. In reality today there is no difference between Jordanians, Palestinians, Syrians and Lebanese. Only for political and tactical reasons do we speak today about the existence of a Palestinian people, since Arab national interests demand that we posit the existence of a distinct "Palestinian people" to oppose Zionism.

For tactical reasons, Jordan, which is a sovereign state with defined borders, cannot raise claims to Haifa and Jaffa, while as a Palestinian, I can undoubtedly demand Haifa, Jaffa, Beer-Sheva and Jersusalem. However, the moment we reclaim our right to all of Palestine, we will not wait even a minute to unite Palestine and Jordan. There are no differences between Jordanians, Palestinians, Syrians and Lebanese. We are all part of one nation. It is only for political reasons that we carefully underline our Palestinian identity… yes, the existence of a separate Palestinian identity serves only tactical purposes. The founding of a Palestinian state is a new tool in the continuing battle against Israel.

Many Palestinians are not even from the area itself. I suggest you read:

The Claim of Dispossession: Jewish Land-Settlement and the Arabs, 1878-1948: Arieh L. Avneri: 9780878559640: Amazon.com: Books

and this article:
The Smoking Gun: Arab Immigration into Palestine, 1922-1931

Many Palestinians live on land that used to have a Jewish community. There were Jewish communities in Hebron and Gaza that don't exist anymore. So the simplistic idea that there was a land called Palestine and that it was owned by Palestinians is false. There were large swaths of barren land, preexisting Jewish communities, Turkish absentee landlords who sold land to the Jewish population, etc.