This phrase is applied when someone has their priorities so out of whack that they'd cry for a dog if it died in a movie but have no problem watching a dozen or more people getting killed, even though
everyone knows that animals are never mistreated on a movie set.
It also can be applied to extremist groups when they talk about saving an animal's life but allowing a human or group of people to die.
Usually said in a pseudo-dramatic or
condescending sense, the phrase is used as a way of saying in a sarcastic manner "Your priorities are all messed up!", because at least a nice woman you can mate with,
what are you going to do with a dog?
John: "I'm watching this movie. It's sad. They killed a dog."
Jack: "
Wait a minute.
The killer just hacked 15 people to death with a chainsaw
ten minutes ago and you're okay with letting them all die but 'don't hurt the doggie!!'?"