KOCHI, INDIA — The dogcatcher tiptoes into a narrow lane carrying a metal wire noose. Someone had spotted a stray dog amid rows of coconut trees a few minutes ago. “Finish that dog today,” one woman calls out from her porch. Another says the dog killed half the ducks in his farm. A third complains the dog has been growling at his 10-year-old son all week. Hundreds of street dogs have been killed in the past year across a state that calls itself “God’s own country,” and is a tourist magnet. Mobs routinely beat dogs to death or hire professional catchers to do the job. Recently a group of men killed several dogs and paraded through the streets with carcasses strung on a pole, dumping them in front of a public building. The bitter man-canine conflict here has alarmed animal lovers across India and drawn sharp criticism from the country’s Supreme Court, which said this month that although dogs cannot become a “menace to society,” widespread killing was unacceptable.