1. I do think that criminals will get guns either way.

In the US, this is probably true. It's worth it to try and prevent this, however there are probably so many guns in circulation that actually preventing them from falling into the wrong hands is an impossible task. In a few years there will be 3D printed guns to worry about, too, as that technology becomes more feasible every day. 

I think a better way to prevent gun related crime is to get to the root causes of the crime itself. Legalizing certain drugs may prevent more gun related crime than additional firearm legislation, for instance. 

2. I believe that a lot of the increased homicides that come from increased gun availability come from improper gun education. Too many stories of kids finding their parents' guns and getting hurt. In such situations, the guns should have been put in a vault or something.

If you lock a gun in a vault or put it somewhere that is difficult to access, then you're negating its usefulness as a tool for self-protection. If the purpose of having a gun is to prevent burglars from invading your home, then you'd want to have it somewhere where it was easily accessible. 

I think that for home security, guns suck. This wasn't the case historically but it is the case now. I think that if someone really cared about home security, they'd install a home security system like the many offered to home owners by private security companies. 

Home security systems aren't a double edged sword like guns are. They aren't going to accidentally kill a loved one by mistaking them for a home invader (or kill anyone for that matter). They also aren't an ever present threat to curious children. Also, the odds of a burglar even bothering to try an invade a home with a security system installed or persisting with the home invasion after the alarms have been tripped is astronomically low. Most burglars just want your TV or your jewelry and they only want it if they can get it without putting themselves at risk. 

3. Crazy people are beyond reason. If someone comes into your home with a gun, being without a gun sounds terrifying. Sometimes it's the only thing stopping you from getting killed

Honestly, statistically speaking, the odds of being in a situation where you have no other choice but to use your gun to defend yourself against a crazy person bent on killing you in your own home are extremely low compared to car accidents or workplace accidents or most other causes of death yet for some reason the former gets way more attention politically than the latter. Unless you live in a really horrible area and don't have the option to move, it should be extremely low on your list of worries and even then, people should consider a security system first and only have a gun on top one if they want to own a gun or if there is a history of extremely aggressive home invaders in the area (very unlikely).

Taking a step back, I think that the argument for owning a gun for protection is a pretty weak one outside of unique circumstances. I think it's a justification that a lot of gun hobbyists use for owning one with historical roots going back for centuries to a time when it really did make sense to have a gun for protection, and that it has little basis in reality today outside of freak incidents which might as well be statistical anomalies. Like cars, guns are dangerous even in the right hands and you're much, much more likely to have an accident with one than you are to successfully use it in self defence.

I think the #1 justification for owning a gun is wanting one. That's it. If you like them and want to own one, knock your socks off, just don't think that it's going to suddenly come to the rescue in a home invasion unless you're some kind of highly skilled professional with combat experience. I think a typical gun owner in that situation would be a liability unless they had some kind of defence training and even then, it might do more harm than good depending on the person. 

Lastly, I'm not arguing against gun ownership in the US. The US is a special case with a long history of firearm ownership and that trying to take guns away would do more harm than good both politically and socially. Gun violence there is just a symptom of an underlying disease that has nothing to do with gun ownership. 

Introducing guns into a society that has no history of gun ownership is a terrible idea, however. I hate when I see Americans argue that countries without gun rights are somehow less free. I'm certain that introducing guns to the general population where I live would make life worse for everyone.