another term/phrase for 'living in somebody else's shoes'

I think you are looking for someone to feel empathy for the other person

Empathy: the action of understanding, being aware of, being sensitive to, and vicariously experiencing the feelings, thoughts, and experience of another of either the past or present without having the feelings, thoughts, and experience fully communicated in an objectively explicit manner

Empathize: understand and share the feelings of another.

Via Merriam-Webster

You should empathize with person C, he's a regular person just like you and me! He's just having a tough time.