The leaders and supporters of BDS (Boycott, Divest, and Sanction) claim that their aim is to place financial pressure on the state of Israel until they unoccupy Palestinian territory and abide by international human rights laws in regards to the people of Palestine. However, many of those who oppose BDS “believe that the real aim of the antisemitic boycott movement is of course the delegitimization of the State of Israel.” 
Israel has been faced with a multitude of existential threats since it was founded in 1948, and BDS is “another attempt to demoralize and destabilize a critical U.S. ally. Compounding these challenges is economic aggression.” 
The argument that BDS is anti-semitic is based off the premise that BDS is denying Jewish people the right to self-determination and an autonomous state of their own. “The idea that all other peoples can seek and defend their right to self-determination but Jews cannot,” declared US Senate minority leader Chuck Schumer in 2017, “is antisemitism.” 
In addition, once that statehood has been achieved, it shouldn't be taken away. The argument as to whether or not the state of Israel ever should have come into existence is no longer relevant - Israel, in the modern day, is home to millions of people with a new and distinct identity and culture. Present day citizens had nothing to do with the conception of the Israeli state in 1948, and "Anti-Zionism proposes nothing less than the elimination of that identity and the political dispossession of those who cherish it.” 
BDS seeks to consistently undermine the comfort, security, and quality of life of Jewish people in Israel who are trying to carve out a safe space for themselves in a world that has targeted them for centuries. Claiming that Israel should be a state for all its citizens, with equal rights for Jewish people and non Jewish people is a form of delegitimization that is inherently anti-semitic.