Man, that was painful to watch.
The guy needs to take more time, energy, and effort with his work.
A rasp to prevent that peeling, multiple cycles of fitting the axe head, seeing where it is tight, rasping it a little to make it fit better, then re-fitting it.
It shouldent be so tight as to NOT take a wooden wedge. Everything needs a wooden wedge. That is how things go together. It is the Metal wedge that is optional.
If you do a good job you don't need a metal wedge.
As far as his first statement. "I've been making firewood for a long time." That says a lot.
You use a maul to make firewood.
You use a Axe to do all kinds of other work.
And what is the deal with the dried up axe handle on the rusted out axe head?
It looks as if he has never sharpened it and leaves it outside.
A few coats of linseed oil a year, and storing it in the garage will prevent the dry rot.
Not a very handy handy-man.
Kinda scary if you ask me.
Edited to add: and how straight can that axe be? Carved half hazardly with only a rough fit?