I agree with HalfPint that your cornbread may be on the dry side. In addition to adding a bit more of whatever liquid you are using, I'd suggest adding an egg. It will add moisture (egg whites are very high in water), as well as binding power. I don't know what your recipe is, but here are a couple of mine to use as a comparison.
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https://food52.com/recipes/17791-cornbread-with-chorizo
https://food52.com/recipes/12558-double-corn-quinoa-cheddar-muffins