It's not "why should" but (at least in my corner of the world) ethics *are* Judeo-Christian.  It doesn't particularly matter if ethical maxims were passed down from Heaven or if Heaven was imagined in concordance with our ethics, what we consider "good" and "moral" is pretty much Judeo-Christian (in most of the western world).

Alluding to religious texts also makes a nice "shorthand" for morality. That way, you don't constantly have to add "i think" or "i feel" to every sentence you say.  We even say "canon, gospel" when we mean immutable, something that can't be questioned.  If you try to do without some meta-touchstone like religious texts, ethics become uselessly subjective.  "Thou shalt not kill"?  Why not?

As I said, ethics are pretty meh.  The Faithful don't need them, and atheists can bend them to suit their needs.