The trouble with meeting someone on the internet is you never know if they’re really able to switch off from it. In the same way that a regular user of Facebook or Twitter gets addicted - online daters find it very hard to resist the temptation to keep looking, winking, or seeing who’s flirting with them.
If anything, someone who can’t resist has insecurities to deal with - and it sounds like your man is one of these. Half the time these people can’t switch off is because they’re afraid of getting hurt, of being left by themselves.
There’s security and familiarity in the e-dating world and it can be hard to leave it - so even though these girls are ‘real life’, they are really little more than porn site characters.
He doesn’t know why because he’s probably not willing to accept that he’s got these insecurities. So, maybe try to reassure him that you’re good, you’ve got a good relationship, and maybe it’d be a nice thing to hang up the flirty websites for a few months.
There is actually evidence to show that it is very easy to become addicted to social media/internet use - because you just get a ‘hit’ of dopamine every time you sign in.
As with any addiction, the only way to break it is to deny yourself (himself) access for long enough to break the addiction. Good luck with that.
If he persists and won’t quit, you’ll have to start looking at it as a destructive/unhealthy relationship that will hurt you in the end. You’d be better getting out and moving on if you can’t encourage him to change this habit.