"She can choose her boyfriend."
Translation:Ella puede elegir a su novio.
"Su novio" is the direct object. He's receiving the action of being chosen. If we use a pronoun instead of "su novio," it would be "Ella puede elegirlo" or "Puede elegirlo a él." Obviously there's more word order variations for the placement of pronouns and object pronouns, but you can see Le(to/for him) doesn't work, because no other object is receiving any action. If she we're choosing a thing FOR her novio, then he would be an indirect object. Puede is inconsequential to the object pronouns, elegir is the verb that matters here, and it's transitive.