Would you stay with a guy who wouldn't ever let you go through his phone?

My partner and I have been arguing about his secrecy over his phone.

His messages come up as "new message" so you cannot read the text unless it's unlocked.

He reckons going onto someone's phone is like getting inside their brain..but if we're in a relationship, whats wrong with me being inside your brain?

We tell each other everything, we're very open and have good communication, but he's SO private about his phone, it makes me think that he's hiding something.

We both have history of past partners who have done us wrong by texting/messing around with other people.

He called me insecure when we were talking about it last night, in my mind, someone who starts throwing insults seems really guilty.

He has always been welcome to use my phone and knows the passcode.

Help. Lol any advice is welcome, just please don't be mean.