The short version:

The area of Palestine and the areas around it has been occupied, and called home, by many different groups over thousands of years.

Jewish people lived in the region in antiquity, likely having split from an indigenous population (rather than anything like presented in Exodus). However, many groups (including Rome) eventually conquered this region, and overtime there were several Jewish diasporas where Jewish people migrated out of the region.

The origins of the Palestinian people is also a bit complex, with some identifying directly with the indigenous people as well.

Of course some Jewish people continued to live in the region continuously, but a huge factor was the persecution that Jewish people faced in Europe and other areas that they migrated to. In 1492, the Jewish people were forced to leave the Iberian peninsula (the Alhambra Decree). The Ottoman Empire, having flourished in the time in between, offered a home to these fleeing Jewish peoples and they settled in various parts of the Ottoman Empire, including Palestine.

While we don't want to paint things as perfect relationship between Jewish and Ottoman peoples, there wasn't constant hatred and fighting either. There were some elements of class, which gave benefits but also took away equal opportunities. Such as the rights for more secular courts, but not being allowed the same titles, roles, etc. that Muslims could gain. But there were periods and examples of unity (Michelle Campos' Ottoman Brothers is a great read on this tension).

The Ottoman Empire was badly weakened by a drought which happened to coincide with the First World War, which is some really poor timing. This allowed for groups within the Empire that wanted autonomy to start making moves, which fractured things further (e.g. The Turks). After the War, the Allies took it upon themselves to start policing the region and creating new nations. Based on popular beliefs at the time, and understanding the troubles which led to WWI, they began to separate people into their own groups figuring it would help. One of these areas was Mandatory Palestine.

In M.P the French and the British controlled how things were run, and the British Prime Minister created the Balfour Declaration which supported Zionists which believed that they deserved to reverse the diasporas and return and have their homeland in the region like they had in antiquity. So he promised them that this could be done as part of M.P. Of course, this angered some other groups that the British had screwed over, including the Turks, who felt there was a sense of favourtism and too much Western influence when this was about self-determination and autonomy.

They tried a bunch of different proposals, some taken with actual steps, some just ideas on paper: including only Jewish people zones, and only Arab people zones (population exchanges were an unfortunately popular idea at this time as well). The more and more that the western powers tried to get involve, the more tensions rised. And as one side would grow more extreme, the other would do so in response. By the 1940s things were incredibly heated, and WWII meant there was only so much attention that could be placed here, but also was heightened by the antisemitism which was at the centre stage of Nazism which made Jewish peoples even stronger in their demand for a home of their own under their own control. War would break out in M.P, and the British firmly decided they didn't want to deal with any of this that they helped create, and slowly withdrew.

M.P. ended in 1948 and as soon as it did a group of Arab states declared war and Israel declared in dependence. A full scale war was on. Israel would win this war, and help to cement a fear of their neighbours wanting their destruction, and help cement a fear of Israel trying to take over and conquer the arab people in the region. These tensions have gone in waves and valleys, https://en.wikipedia.org/wiki/List_of_wars_involving_Israel

So both continue fighting each other, now in less large scale wars but in smaller fights, and instead of looking for ways to make peace and equal concessions, there's just more finger pointing, and thus continued tensions.

Of course, like I said ,this is the short version and it's almost 5k words. It's a very complicated thing, and I haven't even begun to scratch the surface.

I won’t argue with MeatballDom, but do consider carefully the effect of the end of the Ottoman empire on those who had been top dogs (ie: the Arabs of the area the Ottomans called ‘Palestine’)

In the 1920s the formerly colonised occupants (Bedouin, Maronites,Druze, Jews, Kurds etc) were happy the tables had turned. In a world where colonialism is being reevaluated, today’s “Palestinians” can be viewed as the last remnants of the Ottoman imperialists.

As such, the Arab side of the conflict can be seen as a reactionary attempt to restore things to the ‘good old days’. The Israeli side of the conflict is really complex now, as it is not just a Jewish survival thing. It is a multitude of ethnic and political groupings and is too complex/controversial to comment on here.