Answer:
This faulty reasoning is best countered with Newton's First Law.
Explanation:
<em>Newton's First Law</em><em> states that every object or body will remain in its state, be it of rest or uniform motion, unless it is affected by a force. </em>
This means that even while sitting, we are all moving at extreme speeds with respect to the Sun, of approximately 30 km/s (<em>yes, including the bird and the worm)</em>, but we don't even notice because we are all moving at approximately the same speed, and we aren't being affected by a force strong enough that could change our state of being in said extreme speed with respect to the Sun (<em>that is, unless our Earth suddenly stopped moving around the Sun!</em>).
With that being said, when the bird drops down from the limb of the tree, it moves by "adding" a vertical speed from the tree to the ground, but, in reality, the bird is still moving at 30 km/s in a given axis with respect to the Sun, as well as the worm. Now, <em>since the worm didn't "add" a speed to move away from the bird</em> (or, at least, we assume that's what happened), the bird finally catches the worm.
To sum it all up: Yes, the worm still moves at 30 km/s with respect to the Sun, but the bird moves at the same speed, <em>PLUS </em>a given speed from the tree to the ground that helps it get to the worm.