CV axle replacement, old axle is stuck cannot remove it

You need to use a slide hammer. You are correct that this just pulls out but when they are in there for a while they get rusted and don't want to come off easily.

Here is a video of them using one. Clearly you will need to attach yours differently but you get the idea.

You can rent these at a parts store.

https://youtu.be/NgxHZvgckuc

If you don't have access to this then you want to grab hold of the outer shaft and pull it outward in sudden movements. Basically you are looking for the shock to the inner shaft so that it breaks that corrosion loose that are on the splines.

Let me know if you have questions but this is the best way to free them that I have found and I think I have tried them all.