"I'm convinced that if we don't interfere militarily with other countries, they won't interfere militarily with us."

Of course, that simplistic viewpoint might "work" if you are in the middle of Europe. Then again, maybe not.
Now if you were living in Kuwait in 1990, then this cute idea would have been proven wrong.
The US used to strongly believe this, and we had pretty reason to believe this, but then you Europeans kept dragging us into your petty wars. We changed our mind. We realized that other people in other countries might think it's a swell idea to go to war. And wars generally cause other countries to have an interest in the outcome- particularly if these countries are economically involved with these countries.
Now, the US is, of course, working towards a peaceful world. And this isn't a world in which only the US has miltary power. We want other countries [particularly peaceful democracies] to have miltary power and the willingness to use it. In fact, we think it's somewhat unfair that we are forced to spend so much of our treasure on the miltary, whereas our "friends" are taking a free ride.