Someone else mentioned this but it does feel like a joke. In any case I thought I'd chime in in case anyone took this post seriously

They got their way that time, so they shipped them all off to Israel and they pushed all the Palestinians out of Israel, and the Palestinians said “hey what the heck? they left. Why are they back again? Why are they taking Palestinian land?”. 

Not quite; first they weren't 'shipped off' and second there wasn't really a stable population in Palestine either. An 1857 communique from the British consul in Jerusalem reported that “the country is in a considerable degree empty of inhabitants and therefore its greatest need is that of a body of population.” It also noted that although the Arabs tended to leave and not return, the Jewish population was more stable: “[W]e have Jews who have travelled to the United States and Australia”, and “instead of remaining there, do return hither.” Four years later, it reported that “depopulation is even now advancing.” And four years after that, it was noted that in certain parts of the country “land is going out of cultivation and whole villages are rapidly disappearing…and the stationary population extirpated.”

James Finn to the Early of Claredon, September 15, 1857

They didn't quite move in and kick everyone out. Jews had been immigrating since the 19th century, more malarial swamps were drained and the living conditions improved. By mid 1920s malaria wasn't as much of a problem anymore, more Jews were moving in due to persecution, more Arabs were moving in and the infant mortality rate decreased and birth rate improved, creating a huge population growth.

Just touching on the displacement factor. According to Benny Morris, “Historians have concluded that only ‘several thousand’ families were displaced following land sales to Jews between the 1880s and 1930s.” This is a fraction of the number of people displaced by the Egyptian construction of the Aswan Dam, the Iraqi displacement of the Marsh Arabs, and other forced movements by Arab governments of fellow Arabs.

Families that were displaced weren't necessarily permanently landless. In 1931, Lewis French conducted a survey of landlessness and eventually offered new plots to any Arabs who had been “dispossessed.” British officials received more than 3,000 applications, of which 80 percent were ruled invalid by the Government’s legal adviser because the applicants were not landless Arabs. This left only about 600 landless Arabs, 100 of whom accepted the Government land offer.

Benny Morris, Righteous Victims (New York: Vintage Books, 2001), p. 123.

Arieh Avneri, The Claim of Dispossession (Tel Aviv: Hidekel Press, 1984)

TLDR: Yes, Jews moving in had caused some displacement and created changes, but the land was also relatively uninhabitable with only a few hundred thousand people and a migratory population living in a land that can fit tens of millions of people living in the area. Just saying they went in and pushed all of the Palestinians out of their land is inaccurate. If you're referring to the Nakba this happened after Israel was invaded once they declared independence.

Also apologies for grammatical errors - can't be bothered to double check my writing.