I second KJP. You are only pushy if you're pushing. If you are responding to his needs, that's good parenting. As long as it's child-led, it's pretty hard to be "too much too early".

Many teachers have pretty rigid ideas of "developmentally ready", that worship the calendar and ignore the child. If he's enjoying Beast Academy (a pretty awesome program) and wants more, then he's ready for more; don't worry about "confusing" your child with above-age math. If it's too much for him, he will stop enjoying it and wanting it.

If you need some reassurance for yourself that allowing him to accelerate *at his own chosen pace* is good, not bad for him, the research is pretty clear one this one, and summarized here: http://www.accelerationinstitute.org/parents.aspx

Some schools are more flexible, but many of us live in areas that abhor acceleration. Keep working on your school, gently but with confidence, but also recognize that if they won't meet his needs, you may have to do so at home. I don't know how long your on-line subscription lasts, but perhaps if you switched to the paper version your teacher might have a less visceral reaction? A workbook might feel more familiar to her, and Beast Academy, full of cartoon monsters, might seem less threatening than the online drilling machine she may be envisioning.