How do I remove the front axle from a sealed bearing hub? I'm trying to remove the axle from my front wheel to fit it into a box.  But the axle doesn't want to come out.  I've been able to take all the bits off of one side, but I can't remove the ones from the other side, the axle is just spinning while I try and unscrew them.

I expected after I had got one side free that I could just pull it out, but it is not coming out.  

I'm not really sure what to do next, every video and explanation I can find on this says that it should just come out.
The wheel has sealed bearing that are pressed into the hub. Your axle is likely being held in by the bearings. The axle has flanges on the inside that the bearing is resting against. You can try tapping on the end of the axle with a soft faced hammer or even a block of wood. This should dislodge the bearing from the hub. This will also damage the bearing. I would look for a larger box and avoid the hassle of buying new bearings and the tools needed to install them.