I'm a cyclist, and I have dogs. Both of my dogs are Australian Shepherds, they have a strong herding instinct, and one of them is big enough that she can intimidate people who have a pre-existing aversion to dogs (43 pounds). My dogs aren't allowed out of the yard off-leash (or unsupervised), and when we walk them on a MUP they're kept on a short leash - they will look like they are trying to chase cyclists. They're not hunting, they're herding, and I would be devastated if someone was violent against my dog because they mistook her herding instinct for aggression.
That's unlikely to happen as you won't see my dogs off leash anywhere except 3 local parks where they are allowed to be off leash.
As a dog owner the only time I have an issue with my fellow cyclists is when they ride their bikes on foot paths where they're not supposed to be. One of the parks I frequent has mountain bike trails and walking trails, and people will sometimes ride their bikes on the walking trails. I'm not expecting you, my dogs aren't expecting you. If you suddenly come around corner on a foot path at speed, and take offense to my dogs barking at you, you're an idiot (and we're going to have a big problem if you lay a hand on my dogs).
If my dog did somehow manage to run away from home (won't happen, Australian Shepherds are called Velcro-dogs for a reason), and was running along with bikes, I wouldn't judge a cyclist too harshly if she came home with a cleat mark. All the gun talk is a bit over the top, though.
Not to diminish the experience of those who have actually been attacked, or disuade you from trying to defend yourself where it's warranted, it just seems like there is probably a lot fewer genuinely viscious dogs out there than we think (but I'd agree that there is no shortage of irresponsible dog owners), and more frequently than not chasing behaviour is playing, not attacking.