We write about home office working for a living, I'd say. We even had on staff the author of a telework manual who had implemented a similar plan at her previous job. After much wrangling, we were each granted two telework days a month as a compromise. While that sounds good on paper, the initiative failed because it required us to ask permission. Rather than suffer that, staff members began eschewing their telework days, and management scratched its head wondering why, after all the fuss, no one was teleworking.
Point is, sometimes the best-laid arguments fall on deaf ears.
Instead, bide your time, and experiment with more of a back-door approach. First, look for reasonable opportunities to work from home. Inclement weather and natural disasters are great enablers, but too few to count on. While it's tempting, don't target sick days or when the kids are off from school. Plan your telework days carefully, then show the boss how much more work you got done - that might make an impression.