Or in other words, why is the species problem a problem? The "mutually interbreeding kinds" definition seems natural enough; in fact, it's as ancient as the Bible, as shown by Leviticus 19:19
You shall keep My statutes. You shall not let your livestock breed with another kind. You shall not sow your field with mixed seed. Nor shall a garment of mixed linen and wool come upon you.
Even the ancients seem to have adopted the biological species concept! What are the philosophical problems with it as compared to other concepts, like morphological species concept, or the typological species concept?