Here's why:
* Seeds do grow into young plants. This is the fundamental process of germination and plant development.
* "New plant" is a bit ambiguous. While a young plant is technically a new plant, it's not a completely separate entity from the seed it came from. It's the same plant, just in a different stage of its life cycle.
So, it's more accurate to say that seeds grow into young plants, which are the beginning stages of a new plant.