What texting app is he using? If it's iMessage, you would need to be logged into his Apple ID to see the messages. If he's using Verizon Messages+, then when you try to sync with his phone on your computer, his phone will receive a text code that needs to be entered into the computer to confirm the access.
How old is your son? Taking the phone and reading the messages is another alternative, and depending on his age that could be one of your requirements for him having the phone. Who pays the bill?
