Wow, a can of worms there, but yes our involvement certainly has done very little good and a lot of harm. I think a lot of it can be summed up by "Karma", if you subscribe to such a notion. What comes around goes around. For every action, there is an equal and opposite reaction. Do unto others ... you get the idea.
For me, it helps to go back to the beginning in which Abraham had a son Ishmael with the handmaiden Hagar, which was promoted by Abraham's wife Sarah. As the story goes, Sarah was "barren" and this seemed like her only solution. However, in a dream God or the angels promised Sarah would indeed bear fruit. Have faith. At an advanced age, when childbirth was thought to be impossible for a woman of her years, Sarah became pregnant and delivered Isaac to Abraham. The genetic line. Isaac had a son named Jacob (aka Israel), of the "Jacob's ladder" story.
Now I understand this is Biblical genealogy, and not considered 'scientific', but the religions see it this way and so it's their reality. Ishmael's descendants went on to be the Arabic peoples, while Isaac's (and Jacob/Israel) became the Hebrews and later the Jewish people. The Arabic line is that from which Islam eventually emerged. The Hebrews/Jews obviously forged Judaism in the very early times of monotheism (though the Egyptian pharaoh Ahkenaten is usually credited with actually pioneering such beliefs). Much of the basis of Islam is based on the early Biblical prophets, including ... Moses and even Jesus (as a prophet) IIRC. This is why the "three great religions" are said to have a common root. We usually hear the term Judeo-Christian, but Islam shares many of those roots too. In the Middle Ages, you had much conflict between Christians and Jews at certain times, leading to expulsions of the Jews from some European countries, and of course the Spanish Inquisition. So it's not just the current religious hatreds (which are part of the equation, but much more is about land), those have gone on back and forth over many generations. Judaism and Jews were actually tolerated and even thrived many times during the Islamic expansions and the Moors in Spain etc. There is some degree of competition between those religions and their sources, and always will be, as those people's are considered from a Biblical standpoint to be evolved from competing step-brothers.
However, the current problems are much more of a modern phenomenon. The rise of Theodor Herzl's Zionist movement in the late 1800's brought about the realistic possibility of the Jews returning to their homeland, after a nearly 2000 year Diaspora created by the Roman suppression of the Jewish revolt in 66 A.D. and the later Bar Kokhba revolt in 132 A.D. That eventually led to the Balfour Declaration in 1917 in which the British essentially committed to make a Jewish homeland a reality. Around 1920 there began significant Jewish emigration to Palestine based on these ideas and agreements, and at that point the friction between Arabs and Jews started to become entrenched and violent. When Hitler began persecuting Jews, this emigration accelerated for obvious reasons. By the time the U.N. was formed in 1947, there was a significant Jewish population in Palestine - especially from more refugees after the war - and some strong leaders emerged who promoted a new state. So this idea of partitioning Palestine between Arabs and Jews was put on the U.N. agenda, and a plan was conceived. At this point the story could get murky depending on which angle you look at it, but my understanding is that the Arabs did not agree to the partition plan because they felt it was not fair and equitable, and besides, they didn't see any reason to give away "their" lands for the formation of a Jewish state to begin with. The story becomes eerily similar to that of the conflict between white Europeans and the Native Americans (indigenous peoples), with obvious differences. It's the struggle over land and culture.
So, on May 14, 1948 the leaders of the Zionist movement in Palestine declared the new State of Israel, flouting the U.N. partition plan. This triggered the Israeli War of Independence from the Zionist standpoint, and the "Nakba" ("disaster") from the Arab standpoint. It is estimated that 750,000 Palestinian Arabs fled their homes in the violence. The war dragged on for many months, and finally the borders of the new State of Israel were settled by an armistice with the Arab countries. I'm giving the Reader's Digest version, not including the role of the British, and that the war was started earlier in 1948 really. The historical account fills volumes.
The "Six-Day War" in 1967, which Israel initiated pre-emptively based on threats of invasion by Arab countries, was a massive victory for Israel. Nobody expected this, even the Israeli's. They took Sinai and the Gaza Strip from Egypt, the Golan Heights from Syria, and the West Bank and Jerusalem from Jordan. This was the beginning of the "occupation" for the Palestinians, and of Israeli control of the Holy Sites in Jerusalem (though the crucial Temple Mount/Noble Sanctuary is administered by an Islamic council).
One of the issues for peace is the Palestinian "Right of Return" to lands they owned and lived on before the Nakba, and/or a 1967 version for the additional refugees. Many still permanently live in refugee camps. If that were to happen, there would no longer be a Jewish majority in Israel, which contradicts the whole idea of a Jewish State. Ultimately, some form of "land for peace" seems a likely "deal" to find a solution. But whether a One State or Two State version, the demographics of citizenship is a challenge.
I see I have nearly written a book here. But it's really just the tip of the iceberg. And this is my viewpoint and interpretation of history, and to some degree the current outlook, as best I can describe it.