He Never Admits He's Wrong
I'm a big fan of yours as you are very cute and handsome. Anyways, my problem is relationship-oriented. I feel as though I'm always made to be the wrong one and when it goes the other way they justify whatever issue I have with them. When I ask them about this they say that they don't act with an intent to be mean so it is justified, but I don't act to be mean either. I'm someone that can admit fault, but I am starting to have an issue with always feeling like I am the one that is wrong or always doing something that is wrong.
People are going to keep turning things against you and making you feel like you're in the wrong as long as you let them. When you stand your ground, don't take their shit, or even occasionally bite back, they learn their lesson.
It's pretty obvious that he's off-balance as he's totally unwilling to accept responsibility for his actions and instead rationalizing them. What's less obvious is how you're off-balance. You're letting people encroach on your psychological space and subordinate you instead of drawing firm boundaries and saying "HEY. Fucker. Knock it off and back the fuck up." Taking a stand like that is probably as foreign to you as taking responsibility is foreign to him so you're going to need to push yourself until it feels more natural and fluid.
You can and should continue to take responsibility when you screw up, but start drawing some clear boundaries. First, don't allow being wrong or being right to be a big deal. If someone admits fault, accept the apology and move on. If he makes you feel bad and shames you, firmly point it out and tell him to stop.
Second, look out for the difference between explanation and argumentation. Explanation is done calmly and with care. Argumentation is aggressive and done to "win." If you start to feel like he's arguing, justifying, or attacking, point it out and tell him you're just not playing that game anymore. Mature adults are expected to be honest and responsible and resist the maneuvering and posturing characteristic of adversarial lawyers. This is a relationship, not Judge Judy. Don't start again until you really feel like he's not trying to win, just trying to discuss or resolve. If he's someone aggressive who's accustomed to arguing, he might even take a few hours to calm down.
Third, keep some key phrases that foster responsibility in your back pocket, like "what do you imagine I was thinking when you _______" and "can you see this objectively?" and "I'm going to dump you if you don't STFU." And if you hit the point where you feel like you've taken too much responsibility and the other person hasn't taken enough, STOP and make an affirmative decision to stop taking fault until the other person makes some concessions. Will there be times when you mess up and fail to take responsibility for something? Maybe, but that a mistake in the right direction that'll eventually work itself out naturally.
See how it goes. If the guy still doesn't play along, then DTMFA.