A Zionist visitor

It's not an issue of where one's genetic ancestors come from or where they used to live at some point of history. The main point is one's national identity. You are right that there are no pure races, and if traced well back anybody is a genetic relative of anybody else on this planet. However, sometimes people form a certain connecting identity - a tribe, a nation, a people. Sometimes, when separated from the rest of the group or from their national homeland, they lose this connection and assimilate within the local majority. Yet, sometimes it does not happen and people preserve their national identity, their link to their national homeland and the rest of their people. No matter where they are and how much time has passed, they keep this link, passing it from generation to generation.
I'll give you an example. The right of return is a very big issue for the Palestinians. I mean the Palestinians, majority of whom where born outside of Palestine and have never been to Palestine. Those people, who live in London or Toronto, were born there and their children were born there, some of them speak English much better than Arabic, and yet insist that they are Palestinians, demand their right of return to Palestine and promise that they will never abandon this demand and will return eventually no matter how much time will pass. Some would say that this promise is completely unrealistic, but I don't know... It did happen to the Jews after all.