How does invading other nations and setting up democracies in them help expand our freedoms?

It had nothing to do with our freedom. Bush and Cheney had come out against expensive Clinton style nation-building exercises. But then 9/11 happened and everyone wanted payback. We could have carpet-bombed Al Qaida's caves, but that would not have made an effective demonstration. So we invaded Afghanistan and then Iraq, and we would have taken out Iran and Syria too if we hadn't run out of steam. Now we are suffering from buyer's remorse. We broke it. We bought it. We can't afford to keep it. But we might as well try to fix it up a little before we leave and cross our fingers, hoping they won't revert to being our worst enemies again.