How can we reassure our parents not to peek at our mobile phone messages?

Method 1: delete the text message immediately after reading it, so that parents can't peek.

Method 2: Download a software on your mobile phone and set a password lock so that your parents can't open your mobile phone.

Method 3: Just communicate with your parents. Don't do this, it will invade your privacy.

If they don't match, you can implement Method 1 and Method 2.