I think I know what you mean to say, but the term 'assault weapon' has no meaning. A pillow can be classified as an 'assault weapon' if you try to smother someone with it. I am kind of torn on whether or not I agree that some weapons should be illegal to own, but I'll explain my views and why I hold them.
The term 'assault weapon' is very similar to the actual class of weapons known as 'assault rifles.' I think that the media was attempting to create a term that would define weapons that seem militarized, yet aren't rifles.
So what's an assault rifle? Traditionally, it has been a term used to classify weapons that fire a rifle round (like a 7.62 or a 5.56) instead of a pistol round (such as a 9mm or a .357.) The distinction is notable, because rifle rounds are generally far more powerful. Another traditionally distinguishing characteristic is that assault rifles are normally capable of fully automatic or burst fire (more than one round per trigger pull.) In recent years, assault rifles have begun to include certain semi-automatics, like the AR-15.
The second category of weapon is the submachinegun. While they often look and act similar to an assault rifle, they fire pistol rounds and therefore cannot be considered assault rifles. To my knowledge, semi-automatics that fire pistol rounds are not considered to be submachineguns, even when they look identical to their fully automatic counterparts.
Finally, we have handguns, which many people seem to hate. If you don't know what a hand gun is, then you probably aren't smart enough to have read this far, so that's all I have to say about those.
So why is it important to understand the differences? Well if you want to selectively ban firearms, you'll have a better chance of getting people to listen when you are well educated on the subject. In the same way it pisses programmers off when politicians try to regulate the Internet without understanding the slightest thing about computers, it pisses gun owners off when uninformed people try to implement broad, sweeping, policies that result in the banning of guns based on exaggerated or outright fabricated claims of a particular model's capabilities.
In the 90s, a weapon called the Tec-9 became popular in movies. On screen, the gun was always shown to be fully automatic, even though the real one was almost always semi-automatic. There were a few people who managed to modify them to fire on full-auto, but your average gang member probably struggled just to load it. While movies portrayed tec-9 as the ultimate weapon for badasses (because it actually looked pretty cool), the truth is that the gun's popularity was largely due to the fact that it was a total piece of shit, and therefore could be purchased for about 100-150 dollars, which was ridiculously cheap for a 9mm.
Another oft maligned weapon is the AK-47. Unlike most of the world's AKs, the ones that are available in the U.S. are semi-automatic only. Unfortunately, fear sells, causing the media to imply that thousands of people are running around with machine guns. So why do people buy AK-47s if they are semi-automatic? Well, they are reliable, cheap (unless you get an actual Russian made ak, which can cost thousands) and the ammo is inexpensive. They also look just like a normal ak, and some people want a weapon that looks badass, even if it isn't.
Like the AK, the AR-15 is often mistaken for its military counterpart, but the AR-15 is not an M16. The m16/m4 series of weapons can fire full auto or in three round bursts, depending on the model/revision. The AR-15 on the other hand, fires semi-auto only.
While these weapons are often mistaken for automatics, there are some other criticisms that are often mentioned. When the original assault weapon ban was implemented, high capacity magazines and bayonet lugs were two of the defining attributes of an 'assault weapon.' First of all, bayonets are less effective than bullets, and the use of bayonets is so situational that many soldiers aren't issued bayonets anymore (many still do get them, but they are rarely used for combat purposes, and Even then, there is a good chance that it won't be attached to the weapon. Because of this, it's pretty stupid to ban a gun because you can attach a knife to it. If I had to guess, the only reason AR-15s had bayonet lugs was to keep from having to spend extra money manufacturing two different barrels.
Now I'll talk about the only argument that has a bit more legitimacy, high capacity magazines. While it is true that they hold more rounds, super-high capacity magazines (50-200 rounds) like the one used in Aurora, have a slightly higher chance of causing the weapon to jam. That still leaves magazines from 11-30, which are far more common. I can sympathize with the argument that such a magazine contributes to the death count, but a skilled gunman (most aren't skilled) can reload a handgun in under 2 seconds, and a rifle in a similar amount of time. There are videos available on YouTube that show swat/special forces guys loading amazingly fast. It ust takes a little bit of practice.
So basically, I'm not sure what the solution is. Clearly it's not optimal to ban guns outright when there's a hundred million peaceful gun owners in America, yet everyone wants to find a way to prevent mass shooting from happening ever again. Personally, for the reasons I listed, I don't think that the banning of semiautomatic firearms or high capacity magazines is going to be productive. I support the restriction of fully automatic weapons, but they are already illegal to own, unless you go through a process that can take years, that includes a background check.