I think the underlying issue is trying to use logical arguments to make an emotional decision. At the end of the day, polyamory will never fully "make sense" to a monogamous mind. If going poly is going to work, she'll have to understand it from the perspective of your emotional needs.
Quite honestly, no romantic relationship makes logical sense! Making romance work in the long term is work, it requires compromise and forgiveness. You don't have romance because it makes logical sense, you have romance because you're driven to, it feels good, it's comforting. When I proposed to my partner, a friend of mine grilled me for half an hour about why I would want to get married. She successfully shot down every reason I had except one. It felt right, it was what my heart wanted. She accepted that. Marriage isn't logical (unless you do it as a business arrangement because you live in a country with silly laws
and neither is polyamory. They both require more work than being single. So why do any of us do any of it? Because it feels right and our hearts want it.