If you smoked menthol and your quit attempts have gone worse than you expected, the most useful thing to know is that this is a documented pattern rather than a personal failing. Menthol smokers make quit attempts at least as often as everyone else, and succeed at them less often. Something about the product is doing that, not something about you.
Menthol is not a flavouring in the way that word usually implies. It activates the same cold-sensing receptors in your mouth and throat that respond to actual low temperature, which produces the cooling feeling — and, more importantly, a mild anaesthetic effect. It numbs. Cigarette smoke is harsh, and that harshness is a natural brake on how deeply and how often people inhale. Menthol removes the brake. Smokers of menthol tend to inhale more deeply and hold smoke longer, which means more nicotine delivered per cigarette. There is also evidence that menthol slows the rate at which the body clears nicotine, so the nicotine that arrives hangs around longer and the dependence built on it is correspondingly firmer.
Then there is the sensory half, which people underestimate. Thousands of repetitions have welded the cooling sensation itself to the relief of a craving. That means when you quit menthol you are quitting two things at once: a nicotine habit and a very distinctive physical sensation that your brain has filed as part of the reward. Plenty of former menthol smokers describe missing the cold hit in the throat as clearly as they miss the nicotine, and it can catch you out because it does not feel like a nicotine craving at all.
Three things follow from this in practice.
First, do not read your difficulty as weak willpower and do not let a failed attempt convince you that you are especially hopeless. You were using a product engineered to be easier to inhale and harder to leave. That is a different starting position, not a character flaw.
Second, treat medication and nicotine replacement as more clearly worth it, not less. The stronger the dependence, the more there is for a patch, a prescription, or a combination to do. If you have previously tried to quit menthol cold turkey and it did not hold, that history is an argument for adding support next time rather than for trying harder in the same way.
Third, plan for the cooling cue separately. Cold water, ice, strong mints, and menthol lozenges can take the edge off the sensory half of the craving, and many people find them oddly effective precisely because the sensation was doing more work than they realised. One caution: mint-flavoured nicotine products are a mixed choice here, because they can re-anchor the exact pairing you are trying to break. Some people prefer to keep their nicotine replacement unflavoured or fruit-flavoured for that reason.
There is one preparation step some menthol smokers find useful, and it is worth mentioning because it is counterintuitive. Switching to non-menthol for a couple of weeks before your quit date separates the two problems. You keep smoking, so you are not fighting withdrawal yet, but you unhook the cooling cue in advance and give yourself a much less pleasant product to quit. It also tends to reduce how much you smoke, since the harshness brake comes back.
None of this makes menthol impossible to quit — millions of people have. It means the difficulty you experienced was real and had a cause, and the right response to it is a better-supported attempt rather than a more determined identical one.