As a cigar burns, the filler tobacco accumulates oils and tars. The moment a cigar is stubbed out, the wrapper is split, which releases a pungent odor from the exposed filler tobacco. This doesn't happen with cigarettes, which have to be stubbed out.
Premium, handmade cigars need puffing to maintain combustion, unlike cigarettes, which contain additives to keep them burning whether they are puffed or not. Handmade cigars are made only with cigar tobacco, which is also richer and heavier than cigarette tobacco.
The solution—and proper etiquette—is to simply rest your cigar in an ashtray and let it extinguish by itself when you are through with the smoke.