It doesn't. Women are whores is false of the class women, without being logically reducible to the proposition "all women are whores", which is a distinct proposition that is also false. Women raise our children, on the other hand, is true without being logically reducible to the proposition "all our children are raised by women", which is not true. In both statements without an "all", that a normal or common case is intended as the scope of the statement, is understood. In your sentence the statement is false of that normal or common case, and in mine it is true of that normal or common case.
"whereas "birds are like rats" should not imply that all birds are like rats."
Simple, adding a universal quantifier to the front of a statement in general changes the logical meaning of that statement. The original proposition and the new one may both be true, or both be false, or one may be true and the other false - because they are different propositions.
"And lose the silly list of fallacies"
You can go educate yourself about them any time you like, to me they are like breathing or addition, I just assume every intelligent person knows all about them. When they aren't familiar with the terms, they still immediately recognize what they mean and that they are truths as soon as they are explained - just like elementary math. Unless, of course, they willfully resist instruction for tangential reasons.
I will also point out that the additional word "like" in Coulter's statement is a signal that a simile is being employed. Similes compare unlike entities that are alike in some respect, using the point of similarity to illustrate a concept (or for artistic purposes or allusion etc). Coulter did not mean that birds are mammals, or furry, or have long thin tails, or whiskers, or any of a number of other characteristics of rats.
What she meant is transparent from the context, in which she discussed the return of birds to an area in which the existing ones had all been killed or had left. She appeals to a common experience people have had eradicating rats. That is, that killing a bunch of them does not stop there from being rats there a short while later, when the causes attracting them remain.
Just as one may kill many rats intentionally without removing rats from one's environment, one may kill many birds unintentionally without removing birds from one's environment. The simile compares the classes in their robustness with respect to individual deaths. The comparison is entirely apt, unexceptional, and on point. No doubt Coulter also enjoys the way it makes greens bounce off the ceiling - similes can be chosen for such allusive or secondary purposes.
Nowhere in which is there any provision of a "for every" over the class of birds, and nowhere is there the slightest hint of an allusion to the ratlikeness of bald eagles, which is quite entirely your own creation. Based, apparently, on an inability to reason or to tell a piece of well known sophistry from an argument.
"in a set of three women, two women being whores does not permit one to say that "these women are whores"
You can say it, but it would be false. If you said "all these" it would be trivially so. If you said "some of these" it would be trivially true. If you said "most of these" it would be trivially true. When you leave all of those possible quantifiers off, you invite the reader to construct from the context the unifying feature of the class, that is the intended point of reference for the question. As here that feature is not "are whores", the first is false. No one evidentally went out and took pictures of whores for a collection. No one evidentally reached for the best simple description on an intended class, in the predicated term.
"she said "birds", which is the plural of "bird""
Sure, which is what came back after the spill. Not the previous birds, not the exact composition or number, not the whole family of species, but a bunch of birds. Birds as a group that migrates to available habitat are much more resilient than the specific subset of birds there at one time e.g. just before the spill.
"I can't imagine what you're proud of."
What a revealing error. I was ascribing the pride to you. Pride is a weakness, not a virtue.
Oh please. "women raise our children" contains the transitive verb "raise", not the copula. And "all our children are raised by women" is a passive construction to boot, with subject altered. "Women are whores" can be disproven by producing one female non-whore. "Women climb Everest" cannot be disproven by finding one woman who hasn't climbed Everest. You can't replace the copula isomorphously by a transitive verb.
This conversation is over. You called me a liar. Challenged to back it up, you've wasted thousands and words and a good half hour of my time with arguments a high-school student could drive a truck through. Take a long walk off a short pier.