Being respectful is important to me. I wasn't being disrespectful, I was being rude. I said "Ugh," mocked this person's argument (which was in favor of using slurs) by paraphrasing and called it ridiculous; nothing about this denigrates someone's personhood. If I say to someone "your breath stinks, I wish you would brush your tongue" I'm not being disrespectful, I am being rude. If I said "You're gross because your breath stinks" that would be disrespectful. If I called this person a word which is regularly used to dehumanize, that would be extremely disrespectful. The problem is, when you are used to the privilege of being taken seriously, someone being dismissive of your argument feels very shocking and humiliating; you take it personally.
Secondly, the idea that "you catch more flies with honey than vinegar" is flat-out wrong. I have extensive experience with calling people out, and their reaction depends entirely on them (others who regularly engage in calling out also say this is true and I have yet to see a counterexample). I have been polite and had people react with fury, and I've been rude and had people react with concern and a desire to learn. Usually I am polite, but it is not my job to be polite in the face of someone else's disrespect. What usually happens when I argue with someone who is using a slur or otherwise supporting oppression is that that person doesn't change their mind, but others who witness the conversation do. The "catching flies" argument is invariably used by people who just want an excuse not to bother changing.
And oh, the "real activist" argument. There is no wrong way to resist oppression, and my goal is NOT to convert all the people to my way of thinking. My number one goal is to resist oppression in whatever way I can in my individual life. I hope that others are influenced along the way, but I am not an activist for their sake and if they want to be offended by my "PC policing" that's not my problem. I completely reject the idea that I must be an exemplary person for others to realize that oppression is wrong and decide to resist it. I do not need to live up to your standards for oppression to be harmful: that is an objective fact, and it is your job to realize it, not my job to teach you.
The reason I am usually polite is partly because I fear being judged. I have seen what happens with people who are perceived as "too strident" and I am afraid that my friends will judge me that way. I also don't enjoy being rude for its own sake: I am only tempted to do it when I am out of energy to calm myself down and be careful to phrase politely, and too upset to let it pass. I am not proud of being rude to this person, but I am not ashamed either. This was a new experience for me and in the future I intend to be more constructively rude when I am rude (because groaning and mocking is a waste of my time), but I don't intend to make sure I am polite to people using slurs or making oppressive jokes. My politeness is earned by respect and lost by disrespect.