"Palestinian Arabs" as an identity and taxonomy
In answer to user4012, the only Jews that descend from historical Israel are the Mizrahi Jews. The rest are genetically and culturally different. He is in err when he says,
Note that NONE of the sovereign entities in the area were "Palestinian Arabs" - it was either foreign invaders, or Israelites.
To start with, "Palestinian Arabs" are not mutually exclusive with "Israelite". Historical Israelites didn't all flee through subsequent conquest. Many became Christians: all the disciples without exception. Conversion and conquest didn't cease with the ages. The conversion to Islam and conquest by the Muslims further changed the religious landscape. Some people will claim that Arabness only came with the Muslim conquest and thus all Arabs descend from the Arabian peninsula. If that is your frame, things diverge with Muslim conquests, but you're not out of the dilemma: many of the early Jews became original Christians which became early Muslims and subsequently spoke Arabic and identified as Arab. The whole region is Palestine and was until 1948, and the whole region was culturally and genetically impacted by the Muslim conquest.
To state that NONE of the sovereign entities were Palestinian Arabs is just false. In fact, it's substantially more correct to turn that statement on its head,
All of the sovereign entities were mostly (but not entirely) Palestinian Arabs, unless they were foreign invaders.
Some of what we call Palestinian Arabs today are Jews, some Christian; but, most of them are Muslim. Arab-ness wasn't as much an identity then as it was post Nassar as it emerged in opposition to Zionism. Jews didn't identify on ethnic lines, because ethnicity wasn't a "thing" until later, and when it was a thing Jewish-ness was already reborn as multi-ethnic under the Zionist frame.
To summarize, you have one ethnic group the Mizrahi Jews that descend from Israelites. Prior to Zionism erasing what they were, they spoke Arabic and were culturally Arab. Russian Jews -- like myself -- likely converted hundreds of years later and merely identify as Jews for religious and cultural reasons; the identity grew from struggle. Most Mizrahi Jews are Palestinian Arabs. Palestinian Arabs have their roots with the land. Palestinian Arabs are not just Mizrahi Jews, they're also Christians but currently they're predominantly Sunni Muslim. Mizrahi Jews have mostly forfeited their identity as Palestinian Arabs to acclimate into Israeli's right-wing nationalist landscape. The political situation there has supplanted historical and cultural ethnicity with "religious ethnicity" to forge a nationalist frame for colonization which permits inclusion for Ashkenazi, Sephardi, and other Jews into the new "identity."
If that doesn't all blow your mind: I am not a Mizrahi Jew. I have no claim to any land in Palestine. I went to a temple and was a married under a chuppa and the state (Israel) and political platform (Zionism) have nothing to do with me, and I reject them.
Hope that sheds light on the identity and taxonomy issues!
Migration and statehood
If Jews moved to the land, was it their initial plan to move there and make a Jew state?
Many Jews were already on the land, as previously established. Jews not on the land, did not originally intend for statehood. I don't think neither the first nor second Aliyah was predominantly Zionist. It is my understanding the first Aliyah were refugees who sought to coexist and the second were socialists. The third gets a bit obvious and undeniable, and the tone changes. Arab reaction to Zionist terrorism (justified and unjustified alike) and WWII really turned the tides forever and served as a catalyst for the current state of affairs. Certainly by 1920 the tides were changing and by 1930 there was an obvious and vibrant political motive.
What is the justification of Israelis to establish a country in the land?
They claimed it was a "land without a people". They also said it was a requirement to have a "home". Some immigrants were religious (but not all), and claimed ownership based on religious texts. Zionists claimed to be socialists to get the USSR to back them militarily. And, then the Zionists switched sides and aligned with the West seeing the opportunity with President Truman. Each time the "justification" changed: from worldwide socialism, to an American satellite to offset Arab USSR-aligned powers. The list of justifications is miles long.
Then what happened to the inhabitants of the land?
We now know many of them were simply slaughtered and cleansed. The traditional narrative is right in form, but wrong in frame. Many Palestinians fled keys in hand expecting to return. This isn't at all different from the mindset the Jews had when they fled their homes in eastern Europe; it would be a total injustice to say they "just left." The Zionists had well armed and organized right-wing militias, and an air force. The Palestinians didn't. No one wants to die in a losing war, and no one understands the cost of defeat to a right-wing regime.