Relationships have to serve people. If it gets turned around so that the people have to serve the relationship, that means that the relationship isn’t working.
A relationship can be boiled down to two things, rules that you abide by, and roles you play for the other person. A person’s readiness for a relationship is precisely the willingness they have to follow the rules and play the roles.
“Working on a relationship” involves either altering the role the person is playing, or setting additional rules or clarifying them. This all involves clarifying communication. If you want your boyfriend to treat your relationship more seriously, you’re going to have to make a list of things or attitudes you want him to adopt, and then ask him to do these things for you.
“Caring as much about the relationship as I do” is not a clear request. It can not be walked back to an actual definable difference in how he’s supposed to act. Sit down and try to come up with something better to ask him to do. Think of it in terms of rules and roles.
Not in terms of abstract wishes like “I want a boyfriend who really cares about me.” That’s a mushy desire, if you broke up with me and cited that, I’d be like, “oh that’s a girl that doesn’t have a clue about what she wants.” Now if you broke up with me and was like, “You called my mom a stone bitch to her face,” then I can take that and work with it. The role I was expected to play was that of a respectful potential son-in-law. The rule is, “don’t disrespect my family.”
Now, whatever “respectful potential son-in-law” or “don’t disrespect my family” means, has to be worked out between you two. You have to talk it out.
An emotionally-mature guy can discuss these things without getting irrational or shutting down the conversation. If he can’t do that, that’s a perfectly good reason to dump him. But it behooves you to do a little soul-searching on yourself to find out exactly what you want out of him, and to have a conversation about it with him as soon as you do.