Kevin Garvey (Justin Theroux) isn’t a good guy. He knows this deep down, and the audience does, too. He may be a father, a husband, and the chief of police, but he’s a bad person trying his best to find some sort of redemption.
Throughout the first season of The Leftovers (2014), the series often revisits the appearance of deer. Kevin questions whether he's seeing a variety of stags or the same deer resurrecting itself over and over, but the animal's symbolism grows clearer with each visitation: the deer is Kevin.
A woman hits a deer with a car. The Garveys’ kitchen is demolished because a deer gets stuck inside and panics. A pack of wild dogs kills a deer in the pilot, convincing Garvey to help thin the population of dogs. There is a cave painting of two deer on the cover of that mysterious National Geographic magazine Garvey’s father gave him. The same painting, oddly enough, is on the wall of the cabin where Kevin holds Patti (Ann Dowd) captive. A deer wrecks a school, while the children run away screaming about a “monster.” Kevin doesn’t agree -- he sees the deer as himself, just a scared and trapped animal trying to get out.
When the woman hits the deer with her car, Kevin shoots it to put it out of its misery. Immediately following is a shot from a low camera angle, looking up at Kevin with the trees behind him as he considers the doomed animal.
The branches strangely resemble antlers, and the state of the animal represents Kevin’s own confinement.
He feels lost and pointless when he can’t do things for other people. Not saving others, not helping people, he is forced to dwell on his own low-quality life and image. Stags are large and powerful, but when they get stuck somewhere, they’re incapable of figuring out how to escape. Kevin shares this same sentiment. The deer is always looking for a way out, and Kevin is doing the same.
The woman who hit the deer with her car goes on to play a further role in the plot, and the dead deer continues to be a symbol that resonates with the dark events that take place. After shooting the suffering deer, Kevin drives the woman home. She asks if he’s a good person, and he answers “no.” It’s revealed later that the two went to have sex, and this is when the disappearance took place. Kevin was being unfaithful to his wife Laurie (Amy Brenneman) with a woman who disappeared from underneath him, following an association that centered around a deer. Even worse, the deer he shot had an “It’s a Girl!” balloon stuck in its antlers. Later, Kevin finds out that his wife was secretly pregnant with a girl, which disappears from within her during the rapture.
The deer not only is symbolic of his feeling of being trapped -- it also reminds Kevin of the potential grace and beauty of his character, which he is squandering with his bad behavior in an unfulfilling environment. According to Mstars News, Theroux believes the stag to correspond to Kevin's inner self: "In some sense, the stag has to be some kind of - for lack of a better word - spirit animal...Something that represents strength and grace and survival. I don't know what it means in a larger sense for the show, but there is something spiritual afoot," the actor explained.
Symbolically, then, the deer has heavy two-fold connections to the global disappearance that is the foundation of The Leftovers' first season.