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There are two basic tacks you can take on this one. One (and the least likely to be understood by non-gun owners) is the fact that we, the people, are the unorganized militia. By law. It is an old law, but it is still on the books. All men, ages 18-45, except for certain government officials are the unorganized militia. Check your constitutional history, it is in there. That is your basic 2nd Amendment argument. True, and righteous, but not well understood (and often dismissed) by anti-gunners, and those leaning that way.

The other argument is a bit more basic. It boils down to the basic nature of man and freedom. Whenever they ask "why should" whatever be allowed, they are assuming someone else (usually govt) has the moral authority to determine what is best for the individual. One way to frustrate them is to use their own question against them, repeatedly. Because for everything you can think of, and ask "why should it be allowed" you can come up with a perfectly reasonable sounding answer why it shouldn't be allowed. For example,
"why should you be allowed to own a car?"
"I need it to get to work!"
"No, you don't. Take the bus"

The whole concept of what "should be allowed" assumes that we are neither adults nor free citizens. It presupposes that we are all mentally incompetent of deciding for our selves what we should have, and what we should not.

Ask them why they should be allowed to have a job that pays more than minimum wage. Or a house. Or read a book (assuming they can), or, more constitutionally, why they should be allowed freedom of speech. Or religion.
Or why they should be allowed to have children. Or marry who they wish.
Or vote for the candidate of their choice. Pick anything and everything. Pick something they like to do. And be sure to also pick something that has a personal value for them.
Ask them why they should be allowed to do anything besides pay taxes and die!

IF they are somewhat intelligent, they may come back with the argument about the benefits to society of certain dangerous things being banned, like certain (illegal) drugs. And you may reply "oh, like Prohibition?", or you can go with the argument about how illegal drugs in the US are legal in Europe (where basically guns are not legal) or any number of other approaches, but it boils down to who has the right to make choices for you, you? or someone else? The bottom line is that it isn't about what is the right choice for you, it is about whether you get to make the choice. When you give anyone (especially some government bureaucrat) the moral authority to make choices for you, they will take it. And you will never get it back. And your children won't even have that much. They won't even be allowed to give up their right to choose, because by giving up yours, you have taken theirs from them.

Life, Liberty, and the pursuit of Happiness. I care not what course others may take, but as for me, semi-automatics fall under the "pursuit of happiness", as does all other physical property.

After the part about not quartering soldiers in people's homes, the most ignored part of the US Constitution reads "shall not be infringed."!!!!!

Or you could take the (emotionally satisfying) Low Road, and when they ask,
"Why should civilians be allowed to posess semi-automatic firearms?"
Look 'em in the eye and ask "Why should someone as ignorant of history as you are be allowed to keep breathing?"
"Does the word Holocaust mean anything to ya?"

I wouldn't take that approach (at least not without removing the implied threat), but oh, it is tempting sometimes.