Am I doing something wrong?
Nope! At least not according to the Service Manual and from what I remember last time I was poking around in my doors.
You are supposed to pull the rod straight back out of the plastic. Not so easy because of the restricted space. If you have the recommended long needle nose pliers, try spraying some silicone lube on the rod where it enters the plastic and then use the needle nose pliers to try and move the rod back and forth in the plastic to see if you can work the silicone lube in between the rod and plastic. If you can work some silicone in there it might make removal easier. WD40 probably does the job; but, I don't like to use WD 40 on plastic pieces. Silicone is plastic friendly.
When you say steel fishing tape, are you talking about the heavy steel fish tape that electricians use to fish cables through walls and conduit? That was going to be my suggestion, bend a hook in the end of the fish tape, loop the hook around the latch rod right above where the pin enters the plastic and yank back. If that is what you did and it isn't coming out that is one seriously stuck rod.
Since you are a new member, is the car new to you? If so, I am wondering if a previous owner had problems with the latch rod dropping out of the plastic retainer and decided to glue it in place with some CA. Can you move the rod back and forth in the plastic piece at all or does it look like it has been glued in place? If it has been glued, I am at a loss as to how you will get it apart without doing damage.
Edit - Is that blue stuff on the plastic just a grease of some kind or does it look like an adhesive?