Mainly because the region had been under the sway of various empires which were also not Arab - there were communities of lots of religions, Arab, Christian and Jews - and none of them were self-governing under, for example, the Ottoman Turks. So it was seen as a region where new nation states would offer citizens modernity rather than living under foreign empires.
You have to understand here that the modern nation state is a relatively recent construction - even in Western Europe, some modern states simply didn’t exist until the mid- or late nineteenth century — look at the history of Italy, for example. In Britain, the Reform Acts of the early-mid 1800s had only recently established general suffrage even for men. Many parts of the world still lived not in nation states, but under tribal or imperial rule (and not just Western empires by a long way). There were no votes or collective nations or modern states in a lot of the world.
Nationalism and self-determination as a religious or cultural group was thought of as bringing democracy, self-rule and modernity to regions which had lived under other monarchical or absolute rulers from elsewhere, but had never existed as a nation as such. So you can see that lots of peoples and communities within the region saw a chance to create nation states of their own.
The surrounding Arab states in the Levant were all also pretty newly-constructed, too! In the early twentieth century, during the disintegration of the former empires, there was a lot of creating and recreating nations and borders going on all over the place - pretty much everywhere in Africa and Asia. Look at the history of, for example, Syria, Lebanon, or Iran. The Palestine region was not alone in this at all.