"Due process and requirements for warrants are important because it keeps the government honest, and suspending them would cause more government abuse than it would stop crime."

That's fairly vague. I'm not sure what clear distinction you are trying to draw between the 2nd and 4th Amendments.

"But what makes a right to gun ownership important? What does it protect against, and what makes it better than not having that right?"

It can be seen as a right to self defense.

First, consider that your life, or at least your quality of life, depends on the police doing their jobs. To destroy you, the police merely need to make it known that you won't be protected.

There are many examples of this for many different reasons. It could be some political reason why the police chief doesn't want to enforce order in a minority neighborhood. Or, it could be more personal.

Even if the police do make a reasonable effort to protect you, it might not be enough to deter a stalker or someone that you're afraid of. Police generally react after the fact to punish a perpetrator rather than actually protect you, anyway.

You seem to be turning the burden of proof around, to ask why I think we should be allowed a freedom. The social contract says otherwise: we must agree together that a freedom is so dangerous that it should be outlawed.

Honestly, I think you should carefully evaluate whether you think that we are really better off with severe restrictions on guns[1], or whether you are just reacting emotionally to the thought that someone on your block owns a killing machine (which is what guns are, really).

But there are 200M+ guns in the US (numbers aren't precise, but it's about 2 guns per 3 people -- men, women, and children), and we aren't dropping like flies, so you have to look past the emotion. Most gun deaths in the US are suicide, by the way[2] -- and some people argue that is a human right.

[1] The research is mixed on the subject, and I imagine it depends on a lot of factors. To really have an opinion that the right should be removed, you would need to put in a lot of serious effort to research the numbers and convince yourself that people actually would be saved. I have the advantage that I win by default -- I don't need to prove that gun ownership increases safety to hold my opinion, I just need to convince myself that it doesn't increase danger enough to justify restricting it (which is pretty easy considering the low number of gun homicides overall).

[2] http://en.wikipedia.org/wiki/Gun_violence_in_the_United_Stat...