I would leave aside whether it is a fallacy and observe that what you have there is a teleological explanation. These are explanations that appeal to some end in order to account for why something happens, and are one of Aristotle's 'four causes'. Where a reasoning agent is involved, such explanations are perfectly acceptable. For example, if asked, "Why do the hands on this clock go round?" it is quite satisfactory to respond, "In order to tell the time." Of course, the questioner may have wanted to know the efficient cause: what we might today call the mechanism. But the teleological answer is also correct, because a clock is a human artifact and was constructed with an end in mind.
But your example is biological in nature: plants are not artifacts constructed with an end in mind. Because of this, teleological explanations are deprecated within biology. We still sometimes use teleological explanations when talking about biology, but it is understood that this is just a loose way of speaking and that we could rephrase it as an adaptation. For example, if asked, "Why does this bird have this shape of bill?" one might give the answer, "To enable it to catch fish." This appears to be a teleological explanation, but it is really just a loose way of saying that this shape of bill is an adaptation developed by this species of bird that has been positively selected for by its success in catching fish.
To return to your example, "Because plants need water," is not a good answer to "Why does it rain?" because rain is not an adaptation. If anything the reverse is true: plant species adapt themselves to the amount of rainfall in their local climate. So I would say the defect in the answer is that it is attempting a teleological explanation where no adaptation or other plausible account is available to provide an understanding of it.