Are you sure about this? I don't think it's true. I think actually only kids from English speaking parents can attend public English school. Not 100% sure though TBH.
We have french public schools for the same reason you have english public schools in english speaking provinces. It's not rocket science, just common sense.
If you want your kid to go to an english speaking school and deny them from the french culture, no one is stopping you from putting your money where your mouth is.
You do seem to dislike quebec so may I suggest you just move out? It may be better suited for you to live elsewhere.