Progress or pushback?

I've cried so much today I honestly think I am out of tears. I love my boyfriend more than anything. I'm trying to be supportive. I REALLY AM!! But he just argues with me. He's been addicted for over 15 years. He watched porn on his phone so we agreed to block it tonight which we did and we both feel good about. Only I know the password to unlock it. But he absolutely refuses to block it on his computer. Because he never watched it on there. "The problem was the phone not the computer" (it's a Mac so in order to block sites on there I would have to be an admin and he doesn't want that because I would have to enter the password to download songs and other stuff) "you don't trust me that I won't watch it on there" he keeps flipping it around on me. I know he doesn't use his computer to watch. BUT since it's not on his phone anymore what if he gets so desperate he uses the computer.

It's like having a bottle of booze in front of an alcoholic. They won't drink it because it's not their favorite alcohol. But it will still get them drunk so what's stopping them?!

I feel like he's not being 100% committed to changing because of that. But I know blocking it from his phone was really hard to do. I told him how proud of him I am for doing it. But man, I would feel so much better if he would just block it on his computer. I don't know what to do! I hate this! I don't know if in strong enough to take this on.