One is if you're allergic to milk (like my daughter), and the other is if you're Kosher (like my whole family) and you've just eaten meat, and therefore can't have milk for six hours.
Me, I'll wait the six hours and put real milk in my coffee. (But I don't drink real coffee. Just instant decaf, because me on caffeine is like Doc without it, and let everyone who crosses my path beware. I don't even drink brewed decaf anymore, because I don't trust the illiterate idiot who fills the coffee machine in my place of business to recognize the color green. When I asked him the other day, after fighting with everyone all day, if he'd really put decaf beans in that section of the machine which the decaf button pertains to, he shrugged and said "Eh, maybe." So now I go straight to the powdered stuff; if I open a fresh jar, I know that what's on the label is in fact what's in the cup.)
Please note that even so-called "Non-dairy creamers" often have sodium caseinate in them, which is milk protein. If it doesn't say "Pareve" on it, assume it's dairy, regardless of what else it says on the container.