One thing you mentioned is that you want to find a way to deal with this because you love them and want to have a good relationship with them.
You may well find that your relationship to them changes (= improves) when you're an adult and out of the house, even if you don't find a solution for the situation you're in now. Since you say they've grounded you, I'm assuming you're not 18 yet. It's their house, and their rules. If it was their car, it's their rules as well (unless it actually is something where you WERE in the right, like a traffic rule etc). Just because you argue a lot now doesn't mean you won't have a good relationship with them in a very few years.
In the meantime, I think ntrigue's advice on how to respond was really good (I've made a little change):
"I'm sorry you feel that way."
"My mistake, I'll work harder in the future to ensure it doesn't happen again."
"Interesting point, I don't feel that way, but I'll think about what you've said and I hope you'll think about what I've said. I'll be in my room."
When the temperature is rising in a situation where you feel reasonably sure you're in the right, you can try to detach yourself from the emotional aspect of the "conversation". Tell yourself "He's mad right now, but I don't have to be". Just because they're riled up doesn't mean
you have to go there. That will help them calm down, too.
But be critical of how you say things, as well. Do you raise your voice? Are you sarcastic? How do you phrase it when you're accusing them of something? You need to be unfailingly polite, even if they aren't. Otherwise you're only adding fuel to the fire. You need to be honest about anything you may be doing to escalate the situation.
This advice comes from someone who remembers arguing with her parents when she was 17, but who now has a very good relationship with them. And I'm the mother of a 17-soon-to-be-18-yr-old as well. Our difficult discussions go much better if we both try to stay calm enough to make it clear that we are
listening to the other one, even if we don't agree. Disagreement does not have to equal a fight.