If we can forgive the woman's reaction based on an assumed phobia, I think we can forgive the OP for her reaction as well. Just as the woman had no idea if the dog was going to actually lunge at her, the OP had no idea if the woman intended on trying to harm the dog. I think people are more unpredictable than dogs, and since the woman chose not to use her words to convey her concern, there was no good way to interpret her intent.
I'm not finding any rudeness in the OP's response. The woman kicked at her dog. The OP asked her to please not do that, and then reassured her that she had control over the dog. There are so many ways the woman could have responded to that politely, but she chose to snap at the OP and call her dog a "beast".
I do feel bad for people with dog phobias, because the vast majority of dogs they encounter are likely completely harmless. I was bitten (unprovoked) by a dog when I was a kid, but for some reason it only made me afraid of that dog. I have two dogs, and they can be spazzy, so when I walk them I keep very tight control when we happen upon other people. I would be annoyed and a bit bewildered if someone kicked at my dogs as we walked by, although I would probably just give them a "do you eat paint chips?" look and be on my way to avoid any confrontation.