What makes one thing as morally significant as another thing?

Any cause that urges someone to get off their back side and do something costly (even if only slightly) has the curious tendency of warranting lots of push back. Such is the argument Peter Singer presents in his essay “Famine, Affluence, and Morality” of our moral obligation to help those suffering and dying around the world. I cannot help but feeling defensive going through such a read, not only because of how guilty it makes me feel about my lifestyle, but even more so because I know he is right. Regardless of how it makes me feel or its implications for my life, I have to say it is a valid argument.  It has three main premises; suffering and death is bad, we have the moral obligation to help those in such circumstances if we can, and finally he claims we do have the ability to help those suffering and dying. From these premises it naturally follows that we morally, then, ought to help those suffering and dying. However, this argument does leave room for some ambiguity. For example, Singer claims we should be as charitable as possible without sacrificing anything of comparable moral significance (232), but does not clarify what constitutes something as morally significant as another thing. Let’s say my family dog needs a $1000 operation on its stomach or else it will die. At the same time in Ethiopia there are five children who need to be sponsored at a total cost of $1000 dollars or else they will not get the resources they need to survive. According to Singer, distance is not something that takes away from moral obligation, so it is as if these children were my next door neighbors. Then again, my dog is a deeply loved part of the family; but still just a dog. Which case takes precedence? One might jump to say the children should get the money, but when considering how irrelevant to our lives they are, distance seems to have weight in the equation after all. This example may be a little unusual but demonstrates how there are grey areas in an argument Singer presents in a black and white tone.