Oh, all right!!! I guess there's no getting out of this.
Please excuse me for failing to follow through with an explanation. The explanation is, there was no hose to pull out of another hose. The lower radiator hose is about 37.5" long, running from one side of the engine to the other. I didn't know this at first. I searched for the part on the AutoZone website and the part that came up was about 16" of straight hose with one right angle at one end. A subsequent search on the OReilly Auto Parts website turned up the correct hose.
To make a long (embarrassing) story short, I mistook the heat sleeve on that end of the hose for another hose. I spent about 15 minutes trying to twist the pull the hose out of "the other hose" before a male friend of mine who showed up mostly to lend moral support pointed out the reason I was encountering so much resistance.
Did I clear that up for ya? :-O