CHARACTER DEVELOPMENT !!! DING DING DING.
I really LOVE when I get to a point in a role play where I realize that my character needs to face something. Now, I do not mean make a whole sob-story, drama-llama thing. I mean, slowly and gradually pushing them to the point of madness. However, in certain groups, every character is near that point; even if they are an unborn fetus. .//shrugs I do not understand that at all, but I guess people have their quirks... even if those quirks involve being an excessive annoyance.
In order to develop any sort of conflict, you and your roleplaying partner(s) need to know what makes your character tick. Not "annoying pups," or "giddy-happy-whatever girly canine-thing," because no... just no. That isn't realistic even if you aren't going for a realistic character. If they don't enjoy those things, then be more descriptive! What don't they like, specifically, about puppies? Are they too loud, the fact they're small? Have they had a bad experience with puppies in their past? Or perhaps, they themselves knew their own guardians/parents weren't fond of puppies and they learned from that. .//ramble
Back to knowing what makes your character tick; think about it. Place your character in your shoes, or perhaps someone you know. What makes you/them annoyed at the slightest instance? Are they impatient, do they not like crowds, loud noises, the dark, a certain smell or noise? Flesh the character out and test them, that is the only way one can know how to guide your character.
As for fighting and creating conflict, that takes time. It is rarely a "one punch and over with" sort of thing. When did the beef/aggression start? How long has it been an issue? Is there anything specific about the dislike/hatred, is there some psychological reason they do not see eye-to-eye? Think about it. Speaking for me here, I rarely strike at any conflict. Most of my roleplaying characters are peaceful, and if they did have an aggressive past, they have learned from their mistakes. My main character/fursona, Wolfie, is a troubled individual. Yes, she has amnesia and an unpredictable personality; but even then I will never force her to fight.
Ramble over~
Nice topic, by the way. I most likely milked it, aha.