If a state was created by atrocities, etc, as Israel was, that does not lead to the conclusion that it should not exist. A hypothetical country with a pristine origin and history still does not have a right to exist. "Right to exist" itself is a term I've almost only seen used in pro-Israel propaganda. Can you think of a context other than Zionism where the term "right to exist" has even been used?
But Israel is not viable without the active oppression, today, of hundreds of millions of people in the Middle East who are not Jewish.
Iran is the most important strategic threat to Israel. The policies that make Iran threatening to Israel: its refusal to recognize or maintain ties with Israel, its support for anti-Israel groups and its efforts to increase its military capabilities are all popular with the Iranian people (PDF link).
Saudi Arabia has more money than Iran and is closer, and if the people of that country could vote, they would vote for a government that is has hostile to Israel as Iran is, or more. Israel would not be viable if Saudi Arabia was as actively hostile to Zionism as Iran is.
To avoid that, the United States supports a dictatorship over Saudi Arabia's almost 30 million people. The United States does not need the dictatorship to sell oil. A democracy in Saudi Arabia would still sell oil. The United States needs a dictatorship to refrain from using the proceeds of oil sales to threaten Israel. A democracy in Saudi Arabia would not do that. The pro-US dictatorships over the tens of millions of people in Jordan, UAE, Kuwait, Qatar, Bahrain and others in the Middle East in the same way are ultimately maintained today for the sake of Israel.
The United States is a hegemonic power that disregards and acts against the interests of people, especially poor people, all over the world, but it only requires a string of friendly colonial-style dictatorships in Israel's region. The US requires this string of dictatorships in Israel's region because without them Israel is not viable.
Aside, Iran would also have no problem selling oil to the US. The US blocks Iran's oil industry because, and only because, Iran uses or would use the proceeds of its oil sales to support anti-Israel groups. Historically the US oil lobby once competed against the US Israel lobby in an attempt to participate in Iran's oil industry. The oil lobby was defeated in a humiliating fashion.
Another aside, Iran believes it has the right under the NPT to have the same nuclear capabilities countries like Japan have - which is to say while Japan has no weapon, it could build one in an emergency. Israel cannot tolerate other countries in its region even having NPT safeguarded legal Japan-like capabilities. Current US diplomatic efforts against Iran are motivated by this proposition.
Back to Israel. Most people in Israel's region consider Israel an injustice. That does not mean those most people in Israel's region hate Jews, any more than the African opposition to Apartheid South Africa could be explained by hatred for white people. But just as Americans offered rationalizations and justifications for US support for Apartheid South Africa that were not compelling to Black audiences; Israeli, American and other Western arguments for the necessity of Israel as a political majority Jewish state are reasonably not compelling to Middle Eastern audiences.
I'll point out that both Mahmoud Ahmadinejad and Hassan Nasrallah have said that they favor Zionism ending by elections which put in place majority Muslim governments, not by killing anyone. That is how Apartheid ended. Supporters of Israel have a strong interest, because they disagree with the idea of Zionism ending the way Apartheid did, to present opponents of Zionism as more menacing and less reasonable then they are.
For the United States, in the face of the reasonable opposition of most of the people of the Middle East, maintaining Israel requires the active oppression, today, of the hundreds of millions of people in the region who are not Jewish.
For one example, the sanctions, invasion and occupation of Iraq that killed well over half a million Iraqi children would not have been necessary except that a powerful Iraq would threaten Israel more than Iran is acknowledged to today.
Again, the threat Iraq posed to the pro-US oil dictatorships, to the questionable degree that such a threat is real, is only threatening because the US needs those dictatorships for their cooperation with Israel, their refrain from using their resources to oppose Israel. The US does not need dictatorships to sell oil.
The United States did not kill half a million Iraqi children for oil. The United States killed those children for Israel.
To sum up, Israel should not exist as a majority Jewish state not directly because its creation was illegal and immoral. Israel should not exist because its existence as a political majority Jewish state requires the active oppression, right now, of hundreds of millions of people who are not Jewish on behalf of fewer than six million Jewish Israelis.