That’s a very interesting question. I Googled around but couldn’t find any answers, so I turned to the OED.
3. a. The female of certain other large animals, e.g. elephant, rhinoceros, whale, seal, etc., the male of which is called a bull. See BULL n.1 2.
b. attrib. In sense of ‘female’, ‘she-’.
a. A timid, faint-hearted person, a coward. Obs. Cf. COW-BABY, -HEARTED, COWISH a. 2.
b. Applied to a coarse or degraded woman. Also, loosely, any woman, used esp. as a coarse form of address.
c. An objectionable person or thing, a distasteful situation, etc. Austral. and N.Z. slang.
1. a. A large cloven-hoofed, often horned ruminant mammal, Bos taurus (family Bovidae), derived from the extinct Eurasian aurochs and long domesticated for its milk, meat, and hide; a cow, a bull; (in pl.) cattle. Freq. spec.: a castrated adult male of this animal, esp. as used as a draught animal; a bullock.
b. As a proverbial type of strength, brawn, fortitude, obstinacy, etc. Chiefly similative, esp. in as strong as an ox.
My best guess is that the word ‘cow’ is perceived to have more negative connotations/associations as compared to the word ‘ox’, which has more positive connotations e.g. the word ‘cow’ usually brings to mind docile, brainless creatures while the word ‘ox’ brings to mind strong, brawny creatures.
More importantly, I think the real deal here has to do with gender. An ox is usually thought of as masculine creature, whereas a cow usually refers to the female of the species e.g. female elephant, whale, etc.
If you look at the 12 zodiac animals, they’re all male – as opposed to having a tigress, mare, chicken, bitch and sow, we have their male equivalents there.
So I guess it’s really about how the world has been shaped for us, or how the world continues to be shaped – through masculine lenses, through masculine eyes. I’m not particularly in favour of this, so I’ll stick to calling this new year the Year of the Cow.
Thanks for pointing this out and I hope my interpretation helps.