“Penguins only have one partner. When they lose their mate, they never take another one,” a student tells his English teacher Tom Michell (Steve Coogan) during a pivotal moment in the dramatic comedy “The Penguin Lessons.”

Based on a memoir of the same name by the real-life Michell, the film adaptation tells the story of how an adorable penguin gets a new companion in the form of a mercurial yet charming British man who is stunted by his tragic past. Si pinguino, named Juan Salvador, brings anthropomorphized hope to Michell and the elite boarding school St. George’s College in Buenos Aires where he teaches the sons of wealthy Latin American families during a time of intense political upheaval.

The real-life Michell took a liking right away to the oil-soaked penguin washed up on a beach. But the film’s version of Michell is reluctant and, after he realizes the...