I think this question of ‘right to exist’ is a bit of a strange one. The Italy or Russia analogy is quite good here. All countries (except maybe islands) came into being by fighting and one religion/race/ethnicity triumphing over others. And no one questions America/Australia/Peru etc.
However, Israel was formed more recently and in some people’s parents’ generation and in many people’s grandparents’ generation. If I were a Palestinian whose grandparents had been hounded from their home, I would question Israel’s right to exist. There is a genuine grievance there that any civilised nation should address.
OTOH, if you aren’t a Palestinian or know any, then I would question why you would question Israel’s right to exist, other than antisemitism. There are far too many white South Africans etc (may sound bizarre but I know a few) who have massively benefited from historical apartheid in SA and, rather than addressing the ongoing effects of this, for some reason transfer their guilt into constantly attacking Israel.