I have friends who think it's a far-fetched idea that someone could invade my home. They say I'm paranoid to worry about this, and I really don't need to keep a gun. But they don't roll their eyes about the fire extinguisher that I keep in the kitchen. Of course, they say, it makes sense to be prepared for a kitchen fire.
But in reality, a kitchen fire is much less likely to happen. In the US each year there are 3.7 million burglaries, according to the Department of Justice. Of these, roughly one million are "hot" burglaries, occurring when someone is at home. And in 266,560 of those cases, actual violence was done to a family member.
Let's compare this to kitchen fires. The U.S. Fire Administration says that there were 156,500 kitchen fires in the US in 2002.
Now, your definition of home invasion may differ from mine. A "hot" burglary with violence committed against the residents of the home qualifies for me. And you could pick on some of the details like these figures are from 2002 (fires) vs. 2005 (burglary). But it's still clear: home invasions are a real risk, and addressing that risk is not paranoid.