Manifestly and objectively, Bats are not birds. To say so, one must either err or deceive. There is no third choice.
The Bible is not meant to be a scientific description of modern biological categories. Instead, it is often written from the perspective of what we see. In other words, it makes generic categorizations. In this case, the bat is categorized as a bird because like birds, it flies and is similar in size to most birds. If we did not know that it was a mammal, it would be natural to call it a bird. To the Hebrew of ancient times, calling it a bird was perfectly logical. But, in modern times with our science of being able to categorize animal species, we know that the bat is actually a mammal and not a bird.
Also, we must be aware that it is modern science that has a different classification system than ancient times. To the ancients, creatures such as a bat were considered birds since they categorized all flying animals as birds. If that is the category that they used, then they were correct. It is not an error. It is a difference of categorization procedures. You have imposed upon the ancient text a modern system of categorization and then said that the Bible is wrong.