Think of the last time that you ran across a spider, and expressed fear (shrieking, running from the room, shuddering in horror, however you might react to spiders or other creepie-crawlies) and some all-knowing adult tuts and you and quips, "You know, they are more afraid of you than you are of them." That is, essentially, what the quote you cited means. Even people that haven't had experience with animals can relate to that example, so you could approach it from that angle.
To bugs-and all animals-we must appear like aliens would to us; creepy, hairless, huge, making very strange noises and doing strange things with our hands. We are unpredictable; animals tend to be predictable. One animal can smell another, or interpret its body language, and know the drill. But who knows what we are going to do! We might scream. We might go, "Aaaahhhh, how cute!" and try to rub them. We might cage them up, or point shiny metal things at us that emit bright lights (cameras)-a terrifying proposition indeed to animals who are used to the steady light of the sun and moon. If you put yourself in the shoes of the animal, then you can understand just how bizarre we might seem to say, a tiger, who has lived in the wild with his fellow tiger friends his entire life, and feels pretty confident he has life down to a predictable pattern.
One story that is out there that ties in to all of this is called "The Wife's Story" by Ursula K. Le Guin that tells the story of a young family, husband and wife. The wife starts noticing her husband leaving for long stretches of time and coming back acting all strange. So one time she follows him and he starts to transform, or morph, into a strange creature. She is terrified of this creature. Her family follows her out and they all freak out and chase this strange creature into the woods and kill him. Well, it turns out the story was about a pack of wolves, and the "husband" wolf was transforming into a human being. It's like a werewolf story, reversed. That story (I provided a link below; it's a long link, so I hope it works) gives the point of view of what animals must think of us. We are strange, smell strange, act strange, and look strange. And, it scares them.
Anyway, I hope that those thoughts help a bit; good luck with your personal reaction!