the reason why we should save the coyotes is because Coyotes directly or indirectly help to control disease transmission, keep rodent populations in check, consume animal carcasses, increase biodiversity, remove sick animals from the gene pool, and protect crops. wich means if there is a sick ewe(baby lamb) then they can save the lives of many lambs. So why keep shooting them when they can help with disease tranmission this could probly save many people from things like the avian flu and many other diseases. I think we need to be the bigger person and stop killing animals that could save livestock and probly humans but through my research i have found out Coyotes are naturally afraid of humans, but as they get used to living with humans they get less and less fearful, and can become aggressive. Pets, like dogs and cats, look like tasty treats to coyotes, as well. and the more they see us and know what we are doing where we stand and get used to seeing us they get more aggressive like theys two deaths  
 
There have only been two recorded incidences in the United States and Canada of humans being killed by coyotes. One involved a child in Southern California in the 1980s and the other a 19-year old woman in Nova Scotia in 2009. These events, rare as they are, are serious and warrant serious response. theonly two sence 2009. and after all killing coyotes can mean animals they don't kill or seriously wound then alot of others might starve APHIS works to make full use of the resource, which included the donation of 138 tons of goose, deer/elk, and other meat – more than 1 million servings of protein – for people in need. and that's just like saying you might as well through out your dogs because  
 
Domestic dogs, according to the USDA's data, kill 100 percent more cattle than wolves and 1,924 percent more sheep. So I say we save the coyotes!

all info is from google.com