It reminds me of how people make a "purrito" by wrapping a cat in a towel or small blanket in order to safely handle the cat (administer pills, injections, etc.).
And since owls are pretty much just the bird versions of cats, it's fitting.
Reminds me of this classic.
How to Give A Cat a Pill: https://pmc.ncbi.nlm.nih.gov/articles/PMC372253/
Indeed. Cats and owls are a fantastic example of convergent evolution: two species on pretty far vertebrates branches that occupy a similar niche (ambush night predators, small preys) and end up with the same physical appearance- colors, head and eyes shape, even the outer ears shape!
In Chinese, owls are called 「貓頭鷹」, which literally means "a hawk with a cat’s head".