The issue isn’t whether parents love their moody teens, ‘cos they do. It’s whether the moody teens remember that they still love and need their parents. Futile rebellion and confrontation can often be a side-effect of the cocktail of hormones which now swarms through your once adorable child. It’s very easy to rise to every one of the challenges they raise and getting into shouting matches which have the potential to damage your relationship.
You’re not trying to be best friends with your kids at this point in their lives, you’re trying to preserve just the basics of the relationship you used to have. If you manage this then you’ll make sure that, when the terrible teen years are over and done with, you’ll be able to be friends with your kids again.
Be the adult. Don’t surrender a challenge but be calm and just remove yourself from the situation. Tell your teen that you won’t talk to them while they’re being so irrational and that if they want to continue the conversation they’re welcome to once they’ve calmed down. It only becomes an argument if you rise to the bait after all!