There’s more to the action part in Catherine than platforming and puzzle solving. Atlus put enemies in the levels like this bird. Before it pushes Vincent off the tower, you have to defeat it with your pillow.
Sheep, seen in many Catherine trailers, are a common enemy. These stray herbivores will try to bump Vincent to his doom too. You can use your pillow to hit them or an item by pressing square. Items have different effects, like a multi-hit lightning attack as seen in these screenshots.