The Anti-Zionist argument:
"Palestine is a state, recognized by hundreds of countries, so Israel has no right to do Y" in which Y can be bomb them, build settlements, occupy them, etc. But here's where problems start to arise. If Palestine is a state, and let's say for the sake of argument it is, a number of the key Palestinian talking points go away.
Talking Point Number One: The "Right of Return"
Another key talking point of the anti-Zionists is the Palestinian "right of return", which they claim is enshrined in "international law." They will point out that Palestinians are refugees, refugee status is passed down to children, and refugees have a right of return. But according to the UN Convention Relating to the Status of Refugees, the definition of a refugee is,
"a person who owing to a well-founded fear of being persecuted for reasons of race, religion, nationality, membership of a particular social group, or political opinion, is outside the country of his nationality, and is unable to or, owing to such fear, is unwilling to avail himself of the protection of that country". (emphasis added by me)If Palestinians are living in the PA controlled sections of the West Bank and Gaza, and the PA controlled sections are the state of Palestine (as recognized by 100+ countries), how can Palestinians living in Palestine be refugees? The concept is ridiculous. The definition of refugee says above in black and white a refugee is someone living outside his or her country, and the vast majority of Palestinians are living in their country. So they aren't even refugees, much less have a right of return to someone else's country. Don't worry that UNRWA and the UN considers them to be refugees, that's just more proof that the UN is insanely biased in favor of the Arabs, not proof that the Palestinians really are refugees. Nor has the UNSC, the only body on earth that actually makes international law, weighed in on the matter. All we have to go with is the aforementioned handbook. Point this out to an anti-Zionist and watch them sweat.
Talking Point Number Two: The "Stolen Land"
So now let's look at the opposite side of the coin, which can happen if an anti-Zionist backs away from the "Palestine's a state" argument and goes back to the "Palestinians are really Israelis/stateless Arabs who don't have a country and should be allowed to return to the place of their former habitual residence", thus maintaining an argument in favor of the right of return.
But if that is the case, how then can the Palestinians claim ownership over "the Palestinian territories", much less the entire West Bank and Gaza Strip (to say nothing of east Jerusalem)? Individual, stateless people don't own territories, states do. So when settlers build houses in the areas of the West Bank, how can they be "stealing land" from the Palestinians? The answer is: they can't. The only way they could be is if a) a state of Palestine exists and b) Palestine's territory consists of the entire West Bank based on the 1967 armistice lines.
So there's the two step at its heart. There is simply no way the Palestinians can have both a right of return to Israel and a state of Palestine that owns the entire West Bank. Under international law (and indeed basic logic), it's impossible. So ask an anti-Zionist about this some time. I have, and trust me, they don't like it.
Addendum: By the way, there's no contradiction from the pro-Israel point of view. In my opinion, the Palestinians have a "country of their nationality", the country of Palestine, so they don't have a right of return. But that county of Palestine only exists on the territory the Palestinian Authority controls (Areas A and B of the West Bank and Gaza) so Israeli settlements in Area C of the West Bank are not "stealing" land from the Palestinians.