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The Mishna teaches us that all shofaros can be used on Rosh Hashanah except for one that comes from a cow, since a cow has a keren - horn - rather than a shofar. Rabbi Yosi permits the use of a cow's horn, arguing that all shofaros are referred to as keren.
Although the Mishna very specifically teaches the reasoning behind the two opinions on the use of the horn of a cow, two Amoraim nevertheless suggest alternative explanations for the disagreement. Abaye says that the basic position in the Mishna stems from the Biblical requirement of a single shofar - not two or three shofaros.
The horn of a cow is made up of several layers, so it cannot be used (Rabbi Yosi argues that we see the layers as making up a single shofar). Ulla suggests that the basic position of the Mishna is based on the rule ein kategor na'aseh sanegor - a prosecuting attorney cannot become a defense attorney.
Just like the High Priest cannot wear his gold garments into the Holy of Holies when performing the Yom Kippur service, similarly the horn of a cow cannot be used to call out in defense of the Jewish People. Rashi explains that the cow invokes the Golden Calf and therefore is considered a member of the prosecution. In general, gold is seen as representing vanity and a desire for material wealth, which do not seem appropriate for prayers of forgiveness.