At least, that’s a Jungian interpretation. It has also been suggested that the relationship between Batman and Robin has homosexual overtones, especially in the TV show. Carl Jung tended to see homosexuality as a developmental problem, so I’m not sure how he’d depict this particular relationship within his archetypal theory.¹
¹ Jung’s ideas can be too vague and conjectural at times for my liking. To his credit, Jung, himself, admits that he is simply making a modern myth. He doesn’t claim to have the final word. Those interested in his views about homosexuality might find some ideas here.