I have noticed some confusion about what the Yiddish word "goyim" means. It is borrowed from the Hebrew, in which the singular "goy" and plural "goyim" literally mean "nation, nations". This word is used extensively in the Old Testament, sometimes to refer the nation of Israel and sometimes to other nations. It is this latter usage which is the source of its current meaning. The word "goyim" refers to those of "other nations", in other words "non-Jews" or "gentiles". It is not an intrinsicallly pejorative or derogatory term.
I have seen a claim that the word "goyim" means cattle. There very well may have been some Jewish source which said "goyim are cattle" (although this is not, in my experience, a common view among Jews). While such a sentence would be disturbing and insulting, it is not a definition of "goyim". Similarlly, if some Christian source wrote, "Jews are dogs" it would not mean that the word "Jew" meant the same thing as "dog". When people write these sorts of things, they are insulting each other, not defining words.
There is quite enough bad feeling and misunderstanding, without people feeling insulted by words that are not actually insults. In most cases, one should translate the word "goyim" as "gentile" and not see this a negative term.