It is a defence mechanism by people who probably have something to hide.
To be honest if I got my partner checking my phone I wouldn't just say you can look, and it is because why didn't she ask. If it was so important for her to check your phone, she should have asked a permission. It is disgusting. When I was in a "non-healthy" relationship, my ex boyfriend was so jealous. He did not talk to me for 2 weeks because I went out with my friends. He made few other dramas, too. Later it came out that he was flirting with other women during our relationship. It was a good lesson for me; I would never explain myself again as I was always explaining to him.