I'm sorry you're feeling so bad. As parents we all make mistakes. Forgive yourself and move forward. I have raised 5 children and have had my fair share of difficult teens! A valuable lesson I learned along the way is the power of an apology and raw emotion. This is how I would proceed if I found myself where you are. Get him in the car and go for a drive, or some other activity that puts you both in a neutral mood, car rides always worked with my boys. Then just be honest and real. Say something like, "I'm really sorry for losing my temper and saying I hate you. I don't hate you, I will never hate you, I will love you forever no matter what you say or do. What I actually hated was how I was feeling when we were fighting. I don't want to fight with you like that anymore." Be careful not to say he made you mad, or he made you feel a certain way, just own your actions for now. I learned the hard way that teaching our kids how to communicate well was vital. I made a decision that I was never going to be in the place of losing my temper again. I realized temper loss was just feeling helpless and out of control. You're never helpless, and you can always take back control. I made it clear when they wanted something, if my answer was no, they had the option of changing my mind. That's life in the adult world, learning how to get what you need/want. If they argued their point in a way that was disrespectful or rude or any other way un-constructive, I would respond with, "You need to talk to me in a way that makes me want to listen, not in a way that makes me want to send you to your room." They learned quickly that if they used words that angered me, the discussion was over, and the No answer stood. Honestly, I can't tell you how much better it felt NOT having to get angry. When conversations start to heat up with your son, it's ok to say, "We are only getting mad at this point so I'm going to stop this conversation until we feel better." You can choose when to put the brakes on, by doing so you will model good communication for him.
I hope this isn't coming across as preaching!!! I truly feel your anguish. Parenting is a constant learning process, you WILL get through this! All the best and I hope today is better for you both.