In this sentence, "insight" means knowledge—specifically, deep understanding or awareness. So, "fascinating insights into human relationships" refers to valuable understandings or revelations about how people interact. While "perspective" refers more to a personal viewpoint and "perception" is about how something is interpreted, "insight" here implies a deep and often novel understanding of human relationships.

An insight is a deep understanding or awareness of a situation. It might come suddenly. You can even have insight into yourself and the way your own mind works. So here, someone could observe specific aspects of human relationships and understand how they work and what they mean. So of the three words you've offered, I'd reject 'perspective' and say it's more like a combination of 'perception' and 'knowledge' (very roughly).

'Insight' means: the capacity to gain an accurate and deep understanding of someone or something.