Disease
According to the London Hazards Center, cockroaches spread diseases to humans. In addition to the extreme anxiety triggered in some people by the sight of a cockroach, a wide array of physical ailments are transmitted by these creatures. Rather than directly transmitting disease like mosquitoes and fleas, cockroaches contaminate man's world by inadvertently carrying dangerous bacteria to utensils or foodstuffs. Cockroaches are known to carry staphylococcus and salmonella pathogens, and have been implicated in outbreaks of typhus and gastroenteritis. Additionally, these insects cause a number of allergic reactions, including dermatitis, bronchitis, rhinitis (inflammation of nasal membranes) and asthma.
Large Population
One of the more irksome problems regarding cockroaches is that there are so many of them. The most common species of cockroach in America -- the German cockroach -- is a prodigious breeder and is responsible for 98 percent of America's roach infestations. A main reason for the German cockroach's prevalence is that one German female is able to produce 300 offspring. In short order, those 300 cockroaches mature sexually, have their own young and, in a year's time, that single female is responsible for producing approximately 100,000 cockroaches.
Plant Pests
Cockroaches also destroy plants. Cockroaches damage rose bushes, cucumbers, lilies, and the bark and stems of poinsettias. Their proclivity for plant destruction has been bedeviling man for centuries. In the book "Cockroaches -- Ecology, Behavior and Natural History," the authors cite a passage from "Mutiny on the Bounty" in which Captain Bligh washes his ships down with boiling water to keep cockroaches from destroying the breadfruit plants he was carrying from the West Indies. Tomatoes, squash and sweet potatoes are also cockroach favorites.
Odor
One more negative aspect of the cockroach is its smell. According to Safari Termite and Pest Control, cockroaches secrete a substance that contains a strong repulsive odor. Because cockroaches are nocturnal, it is difficult to find them during the day. Extermination professionals, however, often discover the sites of major infestations by following the characteristic cockroach smell. The oriental cockroach, found primarily in Asia, has the most repulsive odor.