While I have not explicitly been asked or told that supporting Israel means that you can’t also support Palestine the following is how I would respond to such assertion.
You must look at the big picture, the whole picture, look at the whole chess board, you have to think multiple moves ahead, as so in international politics. Being pro-Israel doesn’t have you anti-Palestine. While the ideal solution is a two-state solution, where both nations can live side by side in peace and collaboration, that is goal that we have not yet achieved. If you are saying that being pro-Israel makes you anti-Palestine, you are being blinded by your bias. Everyone has biased no matter how much we try to deny it. It’s ok to be biased, you are human, you can’t help but be biased no matter how hard you try, but you must own and be aware of your bias.