I don't have much time these days so I'll just post this even tho it might have been said before. And since I don't have much time this will be my only post on this. PM me if you want me to respond.
Pure Breed: is a breed that has had years and years of work to develop a standard of definition of that breed. This could be size, laying, color, personality, meat, dual purpose, etc.... Most breed encompass definitions for all the above and more. The pure breeds will reproduce the breed to that standard with very few if any deviation.
Hybrid: a mix that is made just for massive production such as the black sex-link, golden comet, red sex-link, rangers, and more. These "breeds" can only be reproduced by breeding Rooster of breed A to hens of breed B any chicks they produce will be Mongrels
Designer "Breeds": are again a mix that is created on purpose to create a specific trait. They do not breed true. there are a couple "breeds" that can pass down a trait and that is Olive Eggers and Easter Eggers. The reason being that egg color is like painting..... you start with White, Blue and Brown. With those 3 colors you can create a mix that will lay a specific color egg. BUT the next generation will throw white layers and brown layers and green layers and everything in between hence they are not a pure breed. and they produce mongrels.
Mongrels: as defined by the dictionary - : an individual resulting from the interbreeding of diverse breeds or strains; especially : one of unknown ancestry
EE's, OE's and any of the production Hybrids are Mongrels.
Mongrels are not bad, it is not a bad word, it has no meaning except a individual of mixed breeding of unknown parentage.
I am a Mongrel, I am a child of mixed heritage as well as unknown heritage. My dogs are mongrels I rescue from death row, most have major behavioral issues.
The mixing of breeds is unpredictable and as long as your ok with the unknown qualities mongrels are sill what ever species they are (dog/cat/chicken)
Now having said all the above.
Pure breed of any species takes years and years of hard work by some dedicated breeder or a group of breeders.
There is the
F1 - Parent or starting birds.
F2 - First generation of mixing
etc etc you get the idea.....
and Here is what the record keeping looks like.
http://archive.org/details/poultrybreedingr299lipp
It is extensive!
You have to keep track of what rooster covered what hen, which hen laid each egg, which chick came from that egg, and you do that hundreds of thousands of times. You might have a rooster that throws white chicks when you want a specific color, oh wait maybe it is the hen that throws that color.... how do you find out? by documenting the results of rooster A with hen A and rooster B with Hen B and then 8 months later the results of rooster B with Hen A and rooster A with hen B, wait 7 months and then try with Rooster C and D or try with Hen C and D oh wait..... where did that chick come from??? Scrap and start over because the chick was perfect to what you want but no idea what set it came from since you lost your breeding book.
Now 18 months later and you might have a small flock for your F2 flock. and heaven help you if none of the combinations throws the right traits because that means you scrap everything back to a new flock of F1's or at the very least adding a new hen/rooster to the F1's
Now after years of hard work documenting every step you finally have a Breed that breeds true to what you wanted as the standard. You get out there and exhibit your new breed to the world one fair/show at a time. maybe if your really lucky you get people to buy that breed from you, then after a few more years there are enough people that want to show them that they start to become standard at a show in the exhibition class (forgive me if incorrect of the name of the class), then the APA or etc says that they can become a breed on their list of legitimate breeds.

You have now invested 15-25 years of your life to create a breed that self produces and maintains the standards you set out for!
Now why would us breeders be mad at the flavor of the month designer breeds? or people selling birds that are "soso" breed when in reality they are mixed? or my personal peeve. calling the chicks/eggs "soso" breed when in reality they have nothing what so ever to do with the breed they claim....
I have to tell people who come to see or buy my birds that the araucana or ameraucana hens are in fact easter eggers even tho the person they bought them from said they were pure bred. These people pay a lot of money for these chicks/eggs, they drive a lot of miles to pick them up and then 6 months later when they want to add a couple more to their flock they find me with my birds for sale. First thing they say is "you birds look nothing like mine" sigh "Oh wait that one looks like mine!" that one is a easter egger.......... This makes for unhappy chicken owners.
I have hatchery stock, pure breeds and mixes, also I am currently creating my own "breed" But I will not call my creations anything but a mongrels/mutt until it starts to conform to the standard I am aiming for. I still have at least 5 years to go before I even get to good F2 step since I can only have 1 rooster for my project and 1 rooster for my Ameraucana's and my mixes that throw pretty colored eggs. Oh and I just lost my project rooster which means I get to start all over again.... oh happy happy joy joy!
so summary....
Mutts are good just of unpredictable traits
pure breeds are good, someone spent years and years working to make them just so.
designer and hybrids are even a lot of fun, just don't expect them to reproduce.... they are a one shot deal... the chicks from them are mutts.
If someone calls it like it is then everything is great.
if someone gives it cutie pie names and sell the snake oil to boot just to make money then us breeders have major issues with that someone.
If your a chicken breed snob, well then your just a snob and most likely a snob in more then just chickens.
as my sig says this is JUST MY OPINION!
I'm off now...
chickielady house is looking great!
judge? lost track but if it was your squeaky toy rooster he is a cutie and will send ya ear plugs soon

Hope everyone is safe and having fun!
Oh and I'm still hoping to setup a chicken swap meet but am still tracking stuff such as who to ask about the parkinglot use etc... no time! I feel like the white rabbit running down the hole!
Edited to fix a few typos and clarify some points.