Why can't I pry out the passenger side CV axle?

SOURCE: Rear Axle Bearing Replacement

That absolutely sounds like an axle (wheel) bearing. Jack up that corner of the truck and grab the top and bottom of the wheel, and shake like crazy. If you have any play whatsoever, it's a sign of a bad bearing (although you could have a bad one and not have any play - it would only mean the bearing isn't worn badly enough to cause looseness in the wheel).

You should be able to remove the axles without opening the diff up. If the axles have c-clips or snap rings on the ends inside the diff, you can usually get the axles out by dismounting them from the hubs and getting them free of all attachment except the diff, and then use a large flat-tip screwdriver as a pry bar. Use it right where the axle body mates to the diff, and lever it while you pull/yank/shake/swear at the axle, and you'll manage to pop the axle out of the diff. Sometimes it takes some time and profanity, but so far it's worked for me everytime.

SOURCE: CV Axle removal and installation

The axle should be able to be removed by using a flat ended pry bar tool with a dull flat end. Or possibly a very large flat screw driver. Put the pry bar between the axle and transmission. With light pressure, the axle should pop out of the transmission. The axle just snaps into the transmission. There should be no need or cause to damage the seal because the seal is inset into the transmission. Just watch what you are doing. As far as replacing the seal, I do not know. I have not had to do that yet, and I have replaced both sides with new boots more than once.

SOURCE: 97 toyota celica outer cv boot replacement passenger side

have you undone the main hub bolt, if yes, there could be two different items holding the cv joint on, one is a small circlip in the joint end, or the other is just like an expanding metal ring again only small. what i had to do to change my one was take the driveshaft out (easier to see whats there) then gently (rubber hammer) hit the CV joint it should then fall off to allow you to change the CV joint. I spent over an hour trying to get the metal ring off, then after taking driveshaft off it was changed and back on in ten mins. Or you can go to a motor factors or similar and get a boot puller, my opinion hammer works better lol

SOURCE: how do i remove the drivers side cv axle on a kia.

The answer is NO... you do not pry it 'OPEN." I'm assuming you've already removed the cotter key and the 1 1/4" nut from the axel hub? The DOJ (Dual Offset Joint) that is inserted into the differential side of the trans has a retaining ring which "COMPRESSES" when you pry the DOJ out using a large pry bar or extra large screwdriver. The same 'COMPRESSION' happens to the ring when you install the new axel.... once fully inserted, the ring 'EXPANDS' inside the differential splines creating enough tension to keep the DOJ in place.

SOURCE: front pass side cv axle removal on 2003 hyundai santa fe

pull swiftly !!! on the axle hub
as its got a big circlip in there & that is why it feels STUCK!
Cheers Rob