"Breeders" is merely descriptive of people who procreate but in no wise should ever have been parents.
I revere good parents, and good parenting. It's a thankless job while it's being done, only appreciated in hindsight when one's experience of the world becomes great enough.
Recently, I observed a woman with a toddler child on an atypical windy and chilly spring day here in Southern California.
The woman was wearing a sweater, a pullover sweatshirt with a blouse underneath. She was warm.
Her child, however, was shivering uncontrollably because all he was wearing was a thin t-shirt and shorts. To perfect the image, this alleged "parent" was yelling at her child to "shut the hell up", causing the child to sob uncontrollably.
Would you honor this person with the name of "parent"? I would sincerely hope not.
Yes, "breeder" is a butt-ugly word. It's a butt-ugly world sometimes.
Demeter: no less than Caesar Augustus called people who didn't procreate "murderers of your own posterity" (at least according to Suetonius). I find the modern usage of the term breeder valid and fair given the general disdain heaped upon people who choose, for whatever reason, not to have children.
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And your rebuttal is well-argued. I certainly know toddlers can be ... difficult. I once spent a morning from hell trying to get my goddaughter's (when she was four) socks just so on her feet and got kicked in the mouth many times before she was pleased with my efforts. My patience was tried, to say the least. Now she's an extremely pleasant, intelligent high school junior. Go figure.
I regret that you find the very existence of the word to be personally offensive, especially since you find no equivalent word for its opposite. I'd like to be incredibly presumptuous and suggest you consider that there is no antonym for the root word "breed" (or "parent", for that matter). That, to me, is incredibly revealing about us as a species.