Welcome to our forum.
I fear that your situation isn't very healthy at the moment. Your boyfriend is saying, "I can see someone new, but you can't," and, "I am the man of the household," and, "We aren't going to talk about it anymore." He is exercising a power imbalance over you, and focusing on his own needs as well as he basks in NRE (New Relationship Energy), neglects you and then claims (and his new girlfriend is guilty of supporting the claim) that you are the one pushing him away.
Since I don't know of any easy solutions to situations like this, I fear that you just have a couple of choices:
- try to convince him to see reason,
- break up with him as amicably as you can.
It's not possible to reason with him if he won't even talk about the problem. I guess my advice is to plead to him to talk about it, and if he still refuses, then advise him you will have to cut the ties if he remains uncommunicative. Try to figure out some reasonable amount of time to wait, something that's fair to you, and if he still won't talk after that much time, I'd suggest you set yourself free. You can always tell him how long you're going to wait, and what the "cut-off" date is.
It's not fair for him to NRE fun while forbidding you the same chance, and furthermore, NRE or no NRE, he still has a responsibility to treat you well and not sweep you under the carpet. If he has any love left for you, he needs to remember that love and make a point to express it. You need reassurance. You need extra time and attention during this sensitive transition. If he thinks you can be taken for granted because you've "always been there," then he is letting NRE carry him way too far.
NRE is all well and good per se. It's the magic of connecting with a new partner. But it's also like an addictive drug, and it can impair judgment. There's a right way to handle it and a wrong way to handle it. Savoring and appreciating it is great; putting your original partner in second place is crappy. It's fine if he needs some time to come to his senses, but he doesn't need forever. He's smart enough to realize when he's neglecting you.
Honey, you need to take care of yourself. You can't always rely on your boyfriend, no matter how long you've been with him. He's not even willing to subject himself to the same fears, jealousies, and insecurities that he's subjecting you to. That's neither healthy nor fair. He needs to take his own personal growth more seriously, and it's not your job to make him see that. All you need to do is speak up for your own rights and feelings, and if he consistently dismisses those, then give yourself a chance to find a new boyfriend who will treat you right.
I regret that this is the best answer I can think of for you. I'm sure you were hoping for some tip or trick that would allow you to get back inside your boyfriend's heart. But I don't think we have such tips and tricks. Each of our hearts are our own. His heart is his own, to open or close as he chooses. Right now, he is choosing to close it to you. I would have to imagine that his choice has caused you to feel very alone.
Give it some time, but then give yourself a cut-off date on which you will embark out on a new path, without relying on him anymore. That's the best advice I can think to give.