I am new to this too, but bear with me.
Perhaps you need to let them know that you can't just shut your feelings off, that you would love to, but it doesn't work that way. You could compromise to not actively pursue a relationship with said person, but that you could remain friends or that you have "permission" (understanding really) to feel that way about them.
I am in a similar situation, actually. I broached the topic of poly to my husband a few months ago and he said something like, "you don't have anyone in mind, do you? That would be different." So we put it off, then I met this wonderful guy and I told him about my feelings. He accepted them but cannot (as of yet) accept the idea of me expressing those feelings sexually.
Your SO has to give a tiny bit, at least in accepting that you can't help the way you feel. You need to accept that he is going to take a while (read as: it feels like FOREVER) to even get used to the idea.
I hope that helped a little