I wanted to address this, too - I’m sure he does care, but like others have said, he likes things just the way they are right now. If this is the future you want with him, then you’re golden, and I wish you all the happiness in the world. 
Somtimes these relationships can last a really long time, when both people are happy with them. I know of one that’s at 12 years and one at 15, both still going strong. One point of view would be why marry, or do anything to change it, when it’s already working. It’s not that he doesn’t like you, or is stringing you along, but he’s already done the marriage thing and didn’t work out, so why do that again. It seems to me like he does really like you but there are other possibilities between breaking up and getting married.
If you like the relationship, then it’s probably fine, and not going to suddenly disappear on you (probably). If you want something else then, that’s tricky and you need to talk to him.
Just curious. Does he have children already? How old?
That aside, it seems that you offer the ideal relationship to him:
You play house.
You are there when he needs you.
Sex.
You are ok or have been ok with him being with others.
You are a great friend.
You hang out.
You just aren’t “her” and he’s told this to you clearly, in words and actions.
He doesn’t want a committed relationship with you. I’ve seen this before, with my Aunt. She was with this guy for like eight or nine years. By all outward appearances they were in a monogamous relationship, but she told him all the time that she felt no commitment to him whatsoever. It didn’t stop him from doing everything for her in a desperate attempt to hang on to her. And one day, something better did come along, and she left him without a second thought, and has been happily married to someone else for several years.
This is your fate. Either accept it or find the strength to walk away.
No children. And yes I do feel I am not “her” guess I needed several strangers to keep pointing that out before I realized that this is what it is. If I were “her” he would not take the chance of hurting me or making me feel bad ever. Sucks but what can you do. The heart wants what it wants and you can not force the issue. Girls have the bad habit of reading more in to actions than are there to justify what they want or are hoping for.
Truly thank you all for your comments. I guess it’s back to dating for me because I do want more. (well after a month or so of crying in my coffee)
When at therapist, start with what this says about you:
“The heart wants what it wants and you can not force the issue.” That’s a few sessions worth of valuable life lessons, for you to move forward with, right there.
Just my opinion. I wish the OP nothing but good luck!
Just as an FYI…
I am on my second marriage. If this doesn’t work out, that’s it. No more marriage. If a woman wants and I am interested I will live together, but married twice is enough.
You might get him to change his mind on this if you wanted children with him or get him so attached to you and then give an ultimatum…but otherwise he just doesn’t see the point of a third marriage. Divorce is hell. He is likely thinking to just live together and enjoy each other and when (er if) it doesn’t work out, part ways.
Don’t be hard on him. He has been through hell.
It’s kinda sad really. I love my wife…very much. However, it isn’t the all-out-crazy-love I had with my first wife. If my second wife wanted a divorce I would be very sad but it wouldn’t be the complete devastation I was left in after my first marriage. Heck, maybe my love for my second wife is more healthy…I don’t know…but it feels different.
I couldn’t imagine a third {shudder}
His aversion to getting married doesn’t cause me to yell RUN, FOREST, RUN.
But his refusal to call you his GF does.
I can understanding being gun shy about marriage if you’re twice-divorced, but we’re not just talking about that. It sounds like what he wants is all the benefits of a relationship with none of the confining rules and obligations that come with that.
This, with a caveat - how long has he been divorced? Anything shy of or right at a year, and I can see him still being gunshy about labels. I was that guy once, but I got over it after a year of being divorced. Anything longer than should be plenty of time to get over that jumpiness.
THIS. I know at least one guy who did the marriage thing twice and is now so over it; he refuses to get married to his long-term girlfriend. However, he does call her his girlfriend! He does acknowledge that they are a couple, and even a long-term couple.
Exactly. I don’t think you have to be married to have a real commitment, but if you’ve been together a significant amount of time and it’s been a year or so since his last divorce? He ought to be ready to call you his girlfriend - unless he thinks of you as a good FWB.
It’'s one thing to not want the legal hassles that come with marriage. It’s another to not wish to acknowledge the relationship as “girlfriend/boyfriend” or give any claim to commitment.
On open relationship might be fine if both people are happy with it, but if either party is not happy, it is just strife in the making.
Girls aren’t the only ones.
Another relevant consideration–perhaps the most relevant of them all–why did his previous marriages end in divorce?
It may be that he got divorced because he can’t handle any long-term committment. If he’s got problems being monogamous for more than a few months at a stretch, I could see why he balks at calling you his GF. He doesn’t want to cheat on you, and the best way around that is to define that relationship so that there’s no such thing as cheating. This is a thing that only makes sense on paper.