I push mine in pretty good. Basically a little over two revolutions and slide off the outer edge. I've never really thought about. I didn't think there was any real way to screw it up.
I absolutely LOATHE those brushes. Absolutely shite. Seriously, they shed their bristles and I agree, make records sound worse. I highly recommend this AT6012. It even does a great job wet cleaning any accidental fingerprints as well. I wouldn’t recommend a full wet clean with this, but I use it dry before every play and it gets all the dust off.