We’re a little late to the game, but here’s the thing about Christmas movies: the holidays aren’t always feel-good and idyllic with everything going according to plan.

Think of the best Christmas movies — “It’s a Wonderful Life,” “A Christmas Story,” those animated TV specials — and you’ll notice there’s a lot of complaining and unhappiness and obstacles to overcome. But by the end of the story, even though some tears were shed, the people we’ve been following for an hour or two have made it through and will be okay.

This is a big part of why “The Holdovers,” the new holiday-set comedy-drama directed by Alexander Payne and written by David Hemingson, is destined to be a Christmas classic.

The warm-and-fuzzies are there, but they pop up in between scenes of deep emotion from lonely people suffering during what’s supposed to be the happiest time of the year. And yet, at the same time, it’s endlessly quotable and hilarious with sharp, witty insults flung regularly because it’s the best ammo these characters have. Sounds like the holidays to me.

The story follows pompous, curmudgeonly teacher Paul Hunham (played by Paul Giamatti) who is disliked by his students, his fellow faculty and the headmaster of a prestigious New England boarding school. With no family and nowhere to go over the 1970 Christmas holiday, Paul remains at school to supervise students unable to go home themselves — the titular holdovers.

After a few days, only one student remains — the trouble-making 18-year-old rebel Angus (Dominic Sessa), an intelligent student whose bad behavior always threatens to get him expelled. Joining Paul and Angus is head cook Mary (Da’Vine Joy Randolph), an African American woman whose son recently died fighting in Vietnam. Over the ensuing two weeks, the three outcasts form an unlikely Christmas family sharing comic misadventures during a snowy holiday.

From the first few seconds of the first preview months before the film’s release, it was evident this was going to be one of those “they don’t make them like they used to” movies. It looks like it’s not only set in 1970 but was made then too with a digital process creating a saturated, grainy look of 35mm film that even has a little artificial wobble and imperfections dropped in from time to time.

Beyond those technical aspects, there are so many small details in the scenes themselves that just make you feel good. The sweaters and coats are big and well-worn, Paul smokes a pipe, they sit on a 1960s-style couch — you know the ones — and watch “The Newlywed Game,” they go candlepin bowling, Paul buys a fifth of alcohol for a couple of bucks and I could go on forever about every shot is filled with small details that put you exactly in 1970.

And while that nostalgic look and feel does complete this production, it’s the characterizations between our three main characters that make it impactful and worth revisiting every Christmas. First of all, Paul and Angus are two ends of the same timeline — a person who’s too smart for his own good and ultimately makes him lead a lonely life. Paul, we learn, has had friends and lovers in the past. But for as long as anyone can remember, he now prefers to sit in his room with a bottle of whatever he can find and drink and read until he falls asleep. Meanwhile, Angus comes from a broken home and has been kicked out of three schools before this one. He’s 18 but is only a junior because he gets into trouble with his less-bright colleagues and superiors, something Paul relates to all too well.

But the real heart of the story comes with Mary, a working-class mother still grieving her son who, despite attending school due to Mary’s employment, is drafted for Vietnam and is killed. There’s an unspoken hatred Mary feels toward virtually everyone at the school — kids of rich white people get to coast by on C’s and go to Harvard while her A student gets the boot.

While Paul, Mary and Angus argue and jab each other with insults, they share their grief and end up having a pretty remarkable Christmas. No, they didn’t have their families, but they had each other, and now we have their company too.