From your Grow tab, you can only connect the bot to pages you're an administrator of. Having permissions in the Business Manager doesn't count here. You need to be an administrator of the Facebook page as stated in the Page Roles section of the page's Settings
If you are an administrator of the page, but you still can't see it in the Publishing section, then you should go into your Business Integrations, remove Chatfuel from there (feel free to do this, despite the warning pop up you'll see - everything will be in order and you want lose any data), and then check the Publishing section again. Make sure to give Chatfuel all the necessary permissions. You should see all the pages you're an administrator of after that.