Many Bible critics will often make the incorrect assumption that the Bible confuses bats with being birds. The reasoning behind this incorrect assumption is due to a misunderstanding of Leviticus 11:13-20. The Hebrew word used at Leviticus 11:13 is ohph, which is sometimes translated incorrectly as birds, and sometimes as fowl. In the past the English word fowl applied not only to birds, but all winged flying creatures such as insects and bats. So, although the word fowl in translation is accurate it is often misunderstood due to the fact that today the English word fowl is somewhat more limited than it used to be, applying to birds only.

The Hebrew word for bat is ataleph.
The Hebrew word for flying creature or fowl (as in all flying creatures including birds, bats, and insects) is ohph.
The Hebrew word for birds in general is tsippohr.
The Hebrew word for birds of prey specifically is ayit.

The Hebrew word sherets is drawn from a root word that means to swarm or teem. In noun form it applies to small creatures to be found in large numbers. (Exodus 8:3; Psalm 105:30) In scripture it first applies to the initial appearance on the fifth creative day when the waters began to swarm with living souls. Genesis 1:20

The law regarding clean and unclean things demonstrates that the term applies to aquatic creatures (Leviticus 11:10) winged creatures, including bats and insects (Leviticus 11:19-31; Deuteronomy 14:19) land creatures such as rodents, lizards and chameleons (Leviticus 11:29-31) creatures traveling on their "belly" and multi-legged creatures (Leviticus 11:41-44).

The English word fowl is primarily used today to refer to a large or edible bird. The Hebrew term ohph, which is derived from the verb fly, applied to all winged or flying creatures. (Genesis 1:20-22) So the Hebrew (ohph) is not so limited in usage as the English word fowl much like the old English cattle in that it once applied to any mobile property.

It isn't about taxonomy it is about language and translation.