First off you're comparing an *ionic bonded* $HF$ with a covalently bonded $\ce{CH4}$.
$HF$ is a stronger acid than $\ce{CH4}$ because its able to furnish out $\ce{H+}$ ions due to its ionic bonding.

So I think you're question boils down to: why is ionic bonding in $\ce{HX}$  (X=Halogen) is stronger than covalent bond. 

This is because in covalent bonding there is only a mutual agreement to share electrons whereas electrostatic attraction in ionic bonding.