grizz3000 is absolutely right - he was trying to use a shell holder for the Lee hand priming tools, which do NOT have the flange on the bottom to lock into a ram. And with the right shell holder, it will be perfectly obvious how it just snaps into place.
FWIW, I've found that RCBS shell holders work just fine in Lee presses (including the Challenger), and probably everybody else's "regular" holders do too, so if you have local access to another brand it would be worth trying. The only thing is that if you're using Lee instruction books they'll use Lee's shell holder numbers, which are NOT the same as RCBS's, and maybe not the same as anybody else's.
BTW, don't pitch that shaved shell holder. The Lee hand primers are outstanding tools, inexpensive, quick and with superb feel. When I'm loading on one of my single stage presses, I frequently use the hand priming tool instead of the one on the press. (It's much easier for me to dump 100 primers in the hand tool, shake, cover and start priming, than to stick single primers into the holder on a press.)