Well, first of all you have to set a definition for what a Palestinian is. You have to remember that Palestine has never been an independent state historically; Arabs living in Palestine in 1947 considered themselves either British subjects, Pan-Arabs, or belonging to another Arab state, e.g, Southern Syrian, West Jordanian, Northern Egyptian, etc.
This becomes very important, because in 1947 the Palestinians really didn't own any land as a nation; they were British subjects until May 15, 1948. The map in question is privately owned land in white that belongs to Jewish owners, and land held in common/public being owned by non-Jewish owners in green.
In the partition plan, a neutral committee divided Palestine by majority population in each region except Jerusalem, which was neutral. The Pan-Arabs at this point rejected the proposal and went to war. The war itself initially went rather well, but with rough UN support, Israel quickly forced back the invaders taking regions they deemed necessary for security. Keep in mind, Palestine still doesn't exist as a nationality at this point; Jordan claimed the West Bank, Syria claimed the heights, and Egypt, Gaza.
With a few more wars for territorial disputes and the last gasps of pan-Arab thought, Palestinianism didn't become a thing until 1964, and even then it was extremely careful on making claims as they would be immediately fighting a war with their Arab neighbors if they did gain a state.
So, right now there is an awkwardness in the region; Egypt would prefer to not deal with Israel post Nassar, Jordan has struck an uneasy defacto peace, Syria is too much of a cluster fuck to do anything. Israel is itself not particularly interested in the land itself in the West bank, where a Palestinian state would likely be, but is more concerned with whether or not this new state would be simply a point to launch attacks on Israel.. and their concern is valid.