Looking closely at the threads that are showing it appears that it may be a reverse thread. (counter clockwise, it is difficult to tell for sure. I do not know why it would be, neither my dewalt nor my bosch are.)
It may also be that the collet is cross threaded.
Since the shaft is already damaged:
Clamp the router FIRMLY to a bench, clamp the shaft FIRMLY ...
It sounds like it is very tightly stuck, in which case similar methods could work as with removing stuck nuts in general:
Penetrating lubricant, such as WD40. Spray it into the nut threads and let it soak in for 15 minutes before trying to loosen the nut.
Heat: use a hot air gun to warm up the nut, it should expand and be easier to remove.
Impact: the idea ...
While the other answer is correct in normal conditions - that is the purpose of the pin.
I would use a bar that fits into the hole in that shaft and a properly fitting wrench as if it has been overtightened it will need some force to undo it.
Using the normal mechanism relies on the strength of the aluminum casting which may break under these conditions. And ...
Rotate shaft until the hole (red arrow)aligns with the pin. (Yellow arrow)Push orange button to interlock pin with hole in shaft. Use appropriate size wrench to turn locking nut(purple arrow). After a couple turns the bit should slip out of the end of the shaft .