CK, I'm a bit reluctant to delve too deep with you on this - precisely for the reasons you've stated - that we won't ever agree. Ultimately, regardless of what my reasons are, or my justifications for why I will never view The 'State of Israel' as 'legitimate', you will always be looking for flaws in my reasoning and perspectives. I don't mind giving you some very basic points/reasons why I don't acknowledge Israel as a legitimate state, but I don't want to engage in a to-ing and fro-ing on each point. Also, fundamentally, I think a large part of it will come down to different readings of history or who we trust as our sources of information.
For example, you listed Peres and Rabin as good ambassadors for Israel. I see them as sustainers and maintainers of a system of oppression and control over Palestinians. OK, when you compare those two to devils like Ben-Gvir or Netanyahu, they're not 'as bad', but they're still deeply troublesome individuals and their role(s) in the Oslo Accords didn't do much to improve the situation for the Palestinians, despite some claims to the contrary.
But if you want to know my brief views on why I view Israel as 'illegitimate', for one, I am anti-Zionist. Two, the Nakba in 1948. Three, the concept of an external population establishing themselves in Arab land and uprooting the indigenous population is an extension of colonial practices and that is something I can't abide. Four, Israel's actions in the Gaza Strip and West Bank contravenes international law and human rights. Finally, the continued and increased support from the USA has allowed Israel to act with impunity and suffer no major tangible consequences.
I have no doubt you will take issue with some of these points, but that's by the by. In a nutshell, these are the reasons why I will never acknowledge Israel as a legitimate state. Its core foundations are based on colonialism and violence.
Ok, here are my thoughts. @brb here's a BIG FAT TLDR warning for you

Your definition of the territory as 'Arab land' is central to where my debate lines will be drawn. I saw also BRB quoted Mahmoud Zahar who said almost exactly the same: "We are the owner of this area - Arabic area. This is well known as an Islamic area." I'm not sure if other posters realise how important this nuance is, and I will try to explain it in my comments. The central thrust of my argument is that it is disingenuous to force the world to believe in what is basically Pan-Arabism, whilst I (and many) and fundamentally disagree with the belief in the divine Caliphate. Without these two beliefs, I don't see any real merit in the political claim made by the Palestinians. I do see merit in the moral claim, which my comments below don't address.
1) Colonial Practices & Illegitimacy
The entire Middle-East is one huge illegitimate bastard-fest of countries fabricated out of thin air during the rewriting of the world order after the fall of the Ottoman Empire and final flourish of British/French Colonialism in the early 20th century (listed below). To raise the question of legitimacy is to throw the entire region into question. It is a series of countries carved arbitrarily out of larger sultanates, kingdoms and empires with lines drawn on maps in conferences thousands of miles away from the people living within those borders. The entire Middle East lacks any semblance of political legitimacy and I would argue that someone who calls into question Israel's legitimacy must also do so for every other country in the region, none of whom apart from Qatar are older than our football clubs. Please note: political legitimacy is not the same as ethnic legitimacy. I am not conflating the two because they are not inevitably linked anywhere in the world. See most modern democratic countries for examples of political legitimacy being granted to people "lacking" ethnic legitimacy. Cf. Southport riots for examples of thugs who don't agree with that point.
Qatar - est. 1878
Jordan - est. 1920
Oman - est. 1920
Turkey – est. 1920
Egypt - est. 1922
Iran - est. 1925 (I'll give you 1905 at a stretch)
Lebanon - est. 1926
Syria - est. 1930
Iraq - est. 1932
Saudi Arabia - est. 1932
Israel - est. 1948
Yemen - est. 1990
2) The question of Political Contiguity
Connected to the above is the question of the amorphous place known as 'Palestine'.
Popular chants such as 'From the River to the Sea' have given rise to the illusion that there has always existed a clearly demarcated country populated by a homogenous group of people who have always identified as 'Palestinian'. In reality, there have only been two occasions in all of recorded history that said river (Jordan) and said sea (Med) demarcated a country distinct from its neighbours: The Hebrew Kingdom of Judea and Samaria of the Bible, and then almost two thousands years later the same landmarks were used for basis of the Partition Plan for Mandatory Palestine & Transjordan.
For the entire interim, the strip of land 'from the River to the Sea' was subsumed under a much more vast Empire or Caliphate: Roman, Byzantine, Ummayad, Abassid, Mamluk, Ottoman and finally British. In fact, the 'River to the Sea' falsehood is so illogical that even Jordan refused to fully relinquish its political claim over that region as rightfully part of Jordan until 1981. i.e., Jordan was denying the existence of a land "From the River to the Sea" for any party, Israeli or Palestinian, until as recently as 40 years ago.
Consider this too: the term 'Palestinian' used in reference to a group of people who were apparently native to that particular area of land only appears in local literature in 1898. Why then? Because a year prior in Basel, the First Zionist Congress convened and agreed that the answer to the 'Jewish question' was a return to Biblical Israel. "Palestinianism" was invented as a response to Zionism.
Prior to that, the notion of homogeneity and contiguity didn't exist, nor had history ever given it cause to. I believe that it is therefore impossible to take seriously the claim that native people living in (for example) Jenin in 1947 had any legitimate claim over land in (for example) the Negev. Nothing connected the two at the time. It would be the equivalent of me claiming that Belgium and France are the same because they happen to be next to each other, mostly speak the same language and were once both controlled by Napoleon.
3) Pan-Arabism, the Caliphate and the Ummah.
Unless I've read too much into your comment, it seems that you are broadly in agreement that the political and geographic label "Palestinian" never really existed. If it did, it would imply that Palestine is the only country in the Middle-East that deserves to have self-determined borders. As above, no other country in the region enjoys this privilege. All borders were drawn under the watchful eye of any or all of the Ottoman, British and French Empires.
The real root of the claim, and one of the reasons why the entire region is so anti-Israel (and will continue to be even if the two-state solution is realised), is either the secular belief in political Pan-Arabism, or in its religious form: the belief in the establishment of a 'Khalifah Rasul Allah', whose lands are sacred Muslim lands and are never to be handed over to or conquered by apostates.
According to both ideologies, 'Palestine' must remain an Arab/Muslim country, either for the purpose of Pan-Arabism, or the upkeep of the Caliphate. Both of these feed into and drink from a concept in Islamic tradition that is entirely alien to the Western mind: the unified Ummah that transcends national identity so that all members of the faith see themselves as one People irrespective of their specific ethnicity or nationality.
This leads to what I believe is a difficult question: By what measure is legitimacy then granted? Which people are considered 'authentic' Palestinians, if the true underlying goal is the establishment of a vast Arab territory across the same vast piece of land that Palestine was for centuries just one small indistinct part of? What do we make of the fact that the Arab population of the country doubled during the 27 years of British rule, largely due to economic migrants who moved from foreign lands to take advantage of the improvements in technology, medicine and job opportunities that the British brought with them?
I don't consider any of those Arabs more 'Palestinian' than the Jewish settlers who arrived in the land before or at the same time, and why should they be? By dint of the fact that they are Arabs and the land is 'Arab land'. Says who? The Ummayads? Does this mean that only Arabs can enjoy independence anywhere in the 7000 miles between Casablanca and Baghdad? By what authority? Should we return Spain to the Arabs, as it was theirs until 1492?
Do we look to ethnicity? If that's the case, how far back should we go? I have Jewish friends who visit the graves of their ancestors buried in Israel over 1100 years ago, to pay their respects. Are they to be denied their ethnic connection to the land, just because once upon a time a colonial power exiled them and carted them off to Europe to enjoy a thousand years of persecution? Isn't that exactly what we're saying has happened to the "Palestinians"? What grants one group's claim legitimacy over the other, when both appear identical and neither can be explained without defaulting to history?
Do we revert to arguments about self-determination? Same questions - when do you measure from? The idea itself is unsurprisingly extremely modern, entering International Law in 1942. By that time, over half a million Jews were living in Palestine. Did they therefore have the right to self-determination? If not, why not?

