I really feel like if I could just get him to understand then we could be so good together.
If you aren't already good together, there is nothing you could get him to understand that will change that.
Abusive relationships usually creep up on you while you are slowly being taught to question your own character, disregard your own needs and feelings and accept gradually escalating abusive behaviour. All the while you are thinking "If only I could be a better person, more organised, more thoughtful, slimmer, didn't have the better job, didn't spend time with my family .... it could be so lovely."
This relationship is based on you seeing some nice bits of him and wishing it could all be like that. It won't. This is the time in a relationship when you see the best in a person. If the best you're going to get is the list that includes him mentioning you to his family it is never going to be good.
What if I've got it wrong and he really doesn't mean to come across this way. How can I tell?
He couldn't even say thank you for the gift you bought him for your first Christmas together. That wasn't unintentional. He simply didn't care about your feelings enough to thank you. You hadn't come up to scratch in the gift-buying stakes and he was letting you know. You've demonstrated to him that, not only will you accept that behaviour, you will also accept completely thoughtless gifts from him.
He was rude about the Valentine's meal you cooked, ignored you for the evening in favour of football and then invalidated your feelings about it in just about the most misogynous way possible by implying that he could sort you out by having sex with you. He showed complete disregard for your feelings throughout the evening, then made out he was doing you a favour by having sex!
If you show him this thread he will probably be nicer for a sort while. However, he won't see the need to sustain it once you're hooked back in. He will then use it against you, probably by ridiculing you for being controlled and manipulated by some nasty bunch of man-haters.
You deserve someone who will treat you as kindly and respectfully as you will treat them.
Being insecure and wanting to avoid conflict doesn't make you hard work but it does make you vulnerable. Stop blaming yourself for his appalling behaviour towards you. You deserve a lot better.
You need to walk away from what is really happening in this relationship before it escalates and stop telling yourself that you deserve the crap he dishes out and, if you could do things better, he will be nicer to you. You don't and he won't.