I met a mom the other day who asked me with such pain in her eyes what to do about her 16 year old daughter who in anger had said to her " I will not speak to you again until I can move out at 18!" That was 2 months ago. The parents stood in front of me that night feeling so hurt and so powerless. The mom bought the silent treatment, hook, line and sinker, and also has not talked to her daughter in these 2 months. Talk about a stand-off. The dad feeling stuck in the middle of the two women he loves, chooses to do nothing rather than look like he is taking sides.
This is an extreme case, but I too remember as a teen, when I felt my mother had misunderstood me so badly that to get back at her I would not talk to her.... forever. Forever turned out to be a few days. Not sure who flinched first, but I know I'm not really good at holding a grudge, but some kids AND some parents are good at grudge holding. Both parties are waiting for the other to apologize, and for two stubborn people this waiting can turn into months as in the mom and daughter above. That is two months too many of wasted time and energy.
When a perceived injustice occurs, and your teen states emphatically that they hate you, and they can't wait to move out, and they will never speak to you again, and then they don't speak to you for days or weeks at a time, and you reciprocate with silence something has gone terribly wrong. Your teen is angry and hurt for whatever reason, as are you. Perhaps you are a stubborn person, who holds on to hurt and find yourself saying:"fine, if she/he doesn't want to talk to me, that's her/his choice, but I can play the same game, and lets see how much they like it!" What kind of model is that? Teens are emotional. Their brain chemistry feeds that flame like air to a fire. Your job is to slowly and carefully find your way into the fire, and get everyone to safety.
You need to keep the door open so that your teen might find their way back in, and save face doing it. They have laid down a gauntlet and now feel obliged to walk it whether they really want to or not. Every night before bed, every morning when they get up, you continue to express your love for them regardless and without expectations. Your teen needs to know that no matter how much they have hurt you, (and perhaps they feel you have hurt them) you always always love them. Texts sent to their phone, cards left on their bed, e-mails sent to their computer, whatever you need to do to let them know that you are ready whenever they are to figure this issue out. Some I get it moments: " I get how angry you are, or I get how hurt you are, or I get you need time, and I respect that. But I love you and I know we can figure out what went wrong here. I can't change if I don't know or understand what can make you so angry with me that you can't even talk to me. I love you, and there is nothing more important to me than figuring out what has gone wrong."This message has to be given without guilt and anger if you truly want to open the doors of communication. Anger breeds anger. Having a child who feels so negatively towards you is unbearable, so much so that many parents don't want to open Pandora's box. Your teen will be brutally honest when the flood gates open and you need to be prepared for that. If your relationship has deteriorated to this extreme, I'm guessing that blame lies with both parties. Modeling ownership of your own part in this allows your teen to do the same. Who flinches first....you do!!