匹
hiki
If you can pick it up, it's 一匹
The picture A creature small enough to hold in your arms or your palm, wriggling along under its own power. Small enough to pick up: 匹. Big enough to look up at: 頭.
Where the picture shows up in 匹
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the one you hold
猫を二匹飼っています。
neko o nihiki katte imasu
I have two cats.
Lifting the cats onto your lap one at a time.
Animals bigger than a person — horses, cows, elephants — take 頭 (とう); birds take 羽 (わ).
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the one running at you
公園で犬が一匹走ってきました。
kōen de inu ga ippiki hashitte kimashita
A dog came running up in the park.
A dog coming at a run across the park lawn towards you.
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the one you reel in
川で魚を三匹釣りました。
kawa de sakana o sanbiki tsurimashita
I caught three fish in the river.
A fish flapping up out of the water on the end of the line.
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the small crawling one
部屋に虫が一匹います。
heya ni mushi ga ippiki imasu
There's a bug in the room.
Your eyes following one small bug crawling up the wall.
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asking how many
この水そうにメダカは何匹いますか。
kono suisō ni medaka wa nanbiki imasu ka
How many killifish are in this tank?
Face pressed to the tank glass, pointing at the killifish one by one.
The sound shifts: 一匹 ippiki, 三匹 sanbiki, 六匹 roppiki.
All of it in one picture
The cat gets lifted onto a lap, the dog comes running, the fish is reeled up out of the water, the bug crawls up a wall, the killifish swim past the glass. All five move under their own power, and all five are small enough that you could reach out and pick one up. 匹 doesn't sort animals by species — it looks only at that liftable size. The moment the animal is bigger than you are, 匹 gives way to 頭.