Slight smell and slight bitter taste of the belly parts of grilled fish

When preparing whole fish at my household, we always slice open the stomach and use a pair of kitchen scissors to snip and remove its guts. We also rinse out the inside of the stomach after removing the guts.

I believe the reason the belly region of your fish tastes bitter is because of un-finished cleaning, just like your local fish-restaurant owner says.

From what I've been told, the bitterness around fish belly is caused mainly by spilled bile when the liver or gallbladder is punctured.

May be caused by improper handling, packaging, rough treatment, excessive pressure (too much weight during storage or transportation), or careless cleaning procedure.

Improper cleaning or removal of the guts may also play a secondary role, though I suspect bile to be the main culprit.

You can some times tell in advance if you notice mustard-yellow spots in the inner walls of the fish belly before or cooking, which tend to turn silvery-greenish after cooking, caused by the spilled bile tainting the meat.

These are usually a indication of bitterness.

You can see an example around the area where the finger is touching the fish. Image source

Food source of the fish may also play a significant role in belly taste.

I have noticed that aquaculture or farmed fish tend to have little to no bitter taste at all, as opposed to wild or free range ones, possibly due to different feeding habits. Farmed ones likely exclusively eat the provided feed (with controlled selection of ingredients for taste and growth), rather than whatever they can naturally find in their environment.

Specifically addressing the pheromone as a cause, I've never personally heard about it, but pork does get Boar Taint (which is pheromone based effect on taste), so it is not totally beyond the realms of possibility, thought I'd expect it to have a widespread effect of fish as well, rather than just around the belly.

I have recently had fresh grilled wild White Seabream (Sargo) and it is one of the worse fish in terms of bitterness, which contrasts strongly with the aquaculture Gilt-Head Bream I can buy at the same vendor, and has absolutely no bitter taste, supporting my food source hypothesis.