I don't think he's wrong to want to be managing all of your workouts (since that's what you're paying him to do), but if you haven't been happy with him lately outside of the Crossfit issue I think it's fine to move on to something else. The most important thing for your health and fitness is that you enjoy the activities you do - that's what will keep you motivated.
while you're talking it out wiht your trainer/boyfriend, make sure you ask him for some free sessions as part of the terms of you staying with him.
but really I think you need to fire him, but I don't think it's because of the ultimatum
I agree with the bolded. You previously said that you tried CF because you were not happy with him, so I think that's more telling than anything. I think you may just need to break up with him, which I know can be super hard.
But I would continue with CF or find another trainer.
I think there's a happy medium somewhere here. I'd quit CF and ask him instead to incorporate crossfit-esque moves into your workout. Tell him it's something you enjoy and if you enjoy it you'll naturally work harder at it. Tell him if he can do that, he has your dedication and that in turn you also need his dedication to be there on time and present.
You are paying him for a service that he isn't providing. Would you pay your stylist, even if she didn't bother to cut your hair? No. Stop paying him, but I would tell him exactly why. Not a discussion regarding how we can make our relationship better. Tell him, this is why I am done paying you. Maybe it will wake him up and not lose the rest of his clientel. If you really feel you need a trainer down the road, find a new one.
(By the way, you look absolutely great in your profile pic!)