Here's a very interesting and wonderful excerpt from Angels (and Demons): What Do We Really About Them? (Ignatius Press; 2004, sixth printing) by Peter Kreeft: The Twelve Most Important Things to Know About Them
1. They really exist. Not just in our minds, or our myths, or our symbols, or our culture. They are as real as your dog, or your sister, or electricity.
2. They’re present, right here, right now, right next to you, reading these words with you.
3. They’re not cute, cuddly, comfortable, chummy, or “cool”. They are fearsome and formidable. They are huge. They are warriors.
4. They are the real “extra-terrestrials”, the real “Super-men”, the ultimate aliens. Their powers are far beyond those of all fictional creatures.
5. They are more brilliant minds than Einstein.
6. They can literally move the heavens and the earth if God permits them.
7. There are also evil angels, fallen angels, demons, or devils. These too are not myths. Demon possessions, and exorcisms, are real.
8. Angels are aware of you, even though you can’t usually see or hear them. But you can communicate with them. You can talk to them without even speaking.
9. You really do have your very own “guardian angel”. Everybody does.
10. Angels often come disguised. “Do not neglect hospitality, for some have entertained angels unawares”—that’s a warning from life’s oldest and best instruction manual.
11. We are on a protected part of a great battlefield between angels and devils, extending to eternity.
12. Angels are sentinels standing at the crossroads where life meets death. They work especially at moments of crisis, at the brink of disaster—for bodies, for souls, and for nations.
Why do people think it's stupid to believe in angels?
One reason is a mistake about themselves: the failure to distinguish between (1) sense perception or imagination (which is a kind of inner sensing) and (2) reason, or intelligence, or understanding. We don't see pure spirits, and we can't imagine them. That doesn't mean we can't know or understand them. We can see and imagine the difference between a five-sided figure (a pentagon) and a six-sided figure (a hexagon), and we can also intellectually understand that difference. We cannot, however, sense or imagine the difference between a 105-sided figure and a 106-sided figure. Both look to us simply like circles. But we can understand the difference and even measure it exactly. So we can understand some things we can't see. We can't see qualities like good and evil either. What color or shape or size is evil? Yet we can understand them. We can imagine our brains, but not our minds, our personalities. But we can know them.
Many who deny angels deny or are uaware of the spiritual half of themselves. Angels are a touchstone of "know thyself". So are animals.