They dismiss it because it's bullshit. Every stop on the slope is not inevitable.

In this particular case, why is the pro-gun community able to prevent changes to gun laws -- despite those laws being deeply flawed and with only a minority of Americans supporting them -- but somehow unable to prevent the floodgates after that?

The response the gun lobby wants to hear is "they gubbermint won't do it because they're scared we'll shoot them!" but it's pure bravado. Grossly negligent gun laws haven't prevented the American government from doing things to its citizens that would make China blush and the pro-gun crowd didn't even change their vote, let alone sacrifice their lives to prevent it.

Because everything is a bullshit slippery slope to them. "Oh you want to get rid of the second amendment? What's next? The first amendment? The fourth?"

Nope. Just the second. It's repealing an amendment, not dabbling with heroin. They're not going to say "oh why not, maybe one more".

Making the "responsible" part of "responsible gun owner" mandatory is not going to cause the collapse of civilisation.