It is the deliciousness of the honey that leads you to gorge on it until you can't face it anymore. Deliciousness leads to eating too much of it, therefore the deliciousness is the problem. You wouldn't eat too much if it wasn't delicious, after all.
Now, I hesitate to use Reddit as an authoritative source, but for an anecdotal demonstration of the principle, you could do worse than this from user/UnIuckyCharms on the subject of 'What's something you'll never eat again and why?':
Buttered popcorn. When I was younger my mom took me to the movies. I complained about not being able to butter the popcorn as I thought she didn't put enough on. Eventually she got annoyed and let me get a new bag and butter it up as much as I wanted on the condition that I ate every single piece. Being 7 and naive I thought I had just won a battle over my mother and proceeded to absolutely drench the bag. Finished it over the course of the movie and made it about 15 minutes into the car ride home before I first started vomiting. The taste stayed in my mouth for days. Liquid shits and a painful stomach for days.
Now the smell of buttered popcorn alone makes me feel sick lol. To this day I avoid the stuff
Now let's look at the text around the lines you quote
These violent delights have violent ends
And in their triumph die, like fire and powder,
Which, as they kiss, consume. The sweetest honey
Is loathsome in his own deliciousness
And in the taste confounds the appetite.
Therefore love moderately. Long love doth so.
Too swift arrives as tardy as too slow.
Friar Lawrence is saying that that intense desires, like u/UnIuckyCharms's desire for buttered popcorn, end with equal intensity, like u/UnIuckyCharms's digestive issues and current aversion to buttered popcorn. The butteriest of popcorn was loathsome in its own deliciousness and in the taste confounded u/UnIuckyCharms's appetite. If they had partaken of the buttered popcorn moderately, they could be enjoying it to this day.
The level of deliciousness is such that it can over-ride a person's good sense in understanding how much of a thing is good for them, that is where the loathsomeness lies. Like the saying
credited to Paracelsus who expressed the classic toxicology maxim "All things are poison, and nothing is without poison; the dosage alone makes it so a thing is not a poison." This is often condensed to: "The dose makes the poison" or in Latin, "Sola dosis facit venenum". It means that a substance can produce the harmful effect associated with its toxic properties only if it reaches a susceptible biological system within the body in a high enough concentration
Therefore a thing which is extremely delicious can lead you to consume so much that it reaches a level of toxicity. Honey has this level of deliciousness.