Map by OP is a lie
The first panel of the traditional version of this map has the biggest lie:
While I presume that the white sections are indeed the land that was privately owned by Jews, the land in green was not privately owned by Arabs.
Only a tiny percentage of land in Palestine was privately owned. The various categories of land ownership included:
Mulk: privately owned in the Western sense.
Miri: Land owned by the government (originally the Ottoman crown) and suitable for agricultural use. Individuals could purchase a deed to cultivate this land and pay a tithe to the government. Ownership could be transferred only with the approval of the state. Miri rights could be transferred to heirs, and the land could be sub-let to tenants. If the owner died without an heir or the land was not cultivated for three years, the land would revert to the state.
Mahlul: Uncultivated Miri lands that would revert to the state, in theory after three years.
Mawat (or Mewat): So-called dead, unreclaimed land. It constituted about 50 to 60% of the land in Palestine. It belonged to the government. ...If the land had been cultivated with permission, it would be registered, at least under the Mandate, free of charge.
By the early 1940s Jews owned about one third of Mulk land in Palestine and Arabs about two-thirds. The vast majority of the total land, however, belonged to the government, meaning that when the state of Israel was established, it became legally Israel's. (I believe that about 77% of the land was owned by the government, assuming 6 million dunams of private land as shown in this invaluable webpage on the topic from which I got much of this information.)
To say that the green areas were "Palestinian" land is simply a lie.
In the case of this version of the map, the lie is even worse, as the implication is that pre-1948 Palestine was an entirely Arab country with no Jews and no Jewish land ownership. Of course, before 1948 the word "Palestinian" more often than not referred to Palestinian Jews, not Palestinian Arabs. For example, the Palestine exhibit at the 1939 World's Fair was entirely Jewish, the Palestine Orchestra was entirely Jewish, the Palestine soccer team was almost entirely Jewish, and so forth.
Now the next one:
While this is a somewhat accurate representation of the partition plan (with the notable exception of Jerusalem, which was meant to be an international city,), it has nothing to do with land ownership. The entire purpose of this map is to make it appear that Israel has been grabbing Arab land consistently, to serve as a bridge between maps 1 and 3. What is not said, of course, is that Israel accepted the partition and the Arabs did not, so as a result Israel in 1949 looked like it does in map 3.
Map 3 is still a lie, however, because in no way was the green land "Palestinian" at that time. Gaza was administered by Egypt and the West Bank annexed by Jordan. No one at the time spoke about a Palestinian Arab state on the areas controlled by Arab states - only in Israel.
In other words, this progression of maps is a series of lies meant to push a bigger lie, and it is tragic that a lot of people believe them to be the truth.
Here is a small attempt on my side to show a more accurate picture of Israel's giving land it controlled up for peace since 1967:
This map shows that Israel gave up control of the Sinai, Gaza, Southern Lebanon and much of the West Bank over the years. Rather than falsely accusing Israel as a land-grabbing rogue state, it accurately shows Israel as perhaps the only state in history that has voluntarily given up more than two-thirds of the areas it controls in exchange for nothing more than a paper agreement - or sometimes not even that. All at the risk of serious security concerns for her people, no less.
This is all because Israel wants, desperately, to live in real peace with her neighbors. This desire is not reciprocated by those neighbors, unfortunately.
The real map shows the truth of Israel's incredible concessions in the often vain hope for peace.