Watched the video and the cotter pin was removed along with the excess grease so that's not an issue.
It appears to me (guessing) that the axle threads may have been damaged when the cotter pin hole was first drilled or installed. I would do a VERY close exam of the cotter pin hole on both sides of the axle looking for damaged axle threads. You may be able to grind down the damaged threads with a small Dremel tool or clean out the cotter pin hole with a small drill.
IMHO a large Crescent or open end wrench would work better on the castle nut instead of the channel lock pliers.
