This is the public explanation I give everyone...
My partner and I's particular dynamic is based on my not wanting to be debased and him wanting a cow girl a la "Monster Musume" (his fave is Cathyl). So, I'm not so much an animal as I am animal-like. A holstaur or minotauress if you're a mythology or DnD fan. A big, sweet, bovine woman.
I'm a companion type -- not cattle but a pet. I keep my person company, offering comfort and support with cuddles and being helpful any way I can. My bf does his best to care for me (comfort, diet, attention). My partner, in particular, loves buying me cute outfits and accessories that relate to my pet-girl side -- animal ears, tail harness, cow-print clothing, collars, jewelry etc. We both have an active wishlist of cowy things to get me. I really want these nice hoof shoes I saw on Etsy...
I often wish I had more chances to wear all that stuff publicly. It makes me feel cute.
Milk production isn't mandatory. He's happy enough just milking me. But I want so terribly to make milk for him and he encourages me when I try and celebrates more than I do when we get drops.
We both have other kinks (some of which we share), but we generally explore them together with the hucow kink as the base. In private, I am his cowy girlfriend 24/7. I wear a bell so he always has a general idea of where I am. I'm usually naked when at home so my udders and teats are easily accessible for teasing and milking whenever he pleases. There is a rule he set out about how I'm supposed to present myself to him if I want to request a milking. But, he is super lenient on that (though I'll still be chided and spanked during the subsequent breeding for not being properly dressed).