Just a newer form of anti-semitism
Antizionists deny the right of the Jewish nation to rule the country of Israel. Antizionists deny that the land of Israel ever belonged to the Jewish nation. (as said in the bible) Antizionists even deny that Jews are a nation, or ever were one. They would often repeat things said by famous anti-semites of the 19-20 centuries, only swaping the word "Jew" with "Zionist". They would refer to each and every citizen of Israel as "Zionist oppressor" and blame him/her for the suffering of the Palestinians. In fact, they would deny simply all of the Jewish history in Israel, and the connection between the Jews and the country, claiming the Arabs ALWAYS ruled Israel and that the evil Zionist just came out of no-where and drove them away.
If all that is true for you, then please, I ask you in any possible way: read the bible. And then read the further history of the land of Israel, that passed from the Babylonians, to the Persian, to the Greeks, to the Romans, to the Byzantians, to the Muslims, to the Crusaders, to the Mamelukes, to the Ottomans, to the British. And tell me which of those great nations remained alive long enough through history to reclaim the land as it's own. And now that you see the only nation that lived throught two thousends years, and ruled the magnificent kingdom of Israel CENTURIES before Islam or Christianity were even formed, do you think your protest against us will do us any harm?