The bottom-right illustration contains 1 large bird.
So the bottom row contributes:
1 + 3 + 1 = 5 birds
Finally:
5 + 9 + 5 = 19 birds
The Answer: 19 🦜
So, I see 19 birds in total.
The reason this puzzle catches people is that the smaller birds are deliberately drawn in a way that makes them blend into the larger birds. Your eyes naturally group the illustrations together rather than treating every individual bird as a separate object.
For example, when you look at the center-top image, your brain may register it as