Whether you call it "pink slime" (the most popular term) or "lean finely textured beef" (the beef industry's preferred name for the substance) that particular emulsified food product consisting of beef trimmings treated with ammonia has become one of the most notorious food additives of the past few decades.
Various forms of meat slurry are not unique. The popular engineered food "chicken nuggets" are produced by a similar process. And those longtime slurries of the processed meat world, hot dogs and sausages (unless you make them yourselves), have always included components that it's best not to think about if you intend to eat them. Meat slurries and chemical additives are among the reasons I mostly eat food from plants, and overwhelmingly buy those foods in a form which makes them easily recognizable to me. The tomatoes I buy or grow look like tomatoes. The beans are clearly beans. Even the flours I buy tend to look like what they are purported to be, and if I buy organic whole wheat the likelihood that it is really ground grain is high enough for me to accept.
The argument that pink slime is being treated unfairly may have a grain of truth to it. Pink slime has the disadvantage of being pink and slimy. It also had the misfortune to have its derisive popular name stick. The likelihood that the industry's chosen name, "lean finely textured beef" is ever going to gain currency is nearly zero. But on the other hand pink slime is probably no more unsafe (or in my opinion unappealing), than the tens of thousands of other highly processed food-like products foisted upon the public every year.
There are two interesting arguments I've seen advanced defending pink slime.
The first is that the controversy is killing companies, and consequently jobs. That's true, but industries are hurt by negative publicity all the time. The same argument could be used to defend the tobacco industry, or to remove toy safety regulations. Consumers have indicated clearly that they don't want to eat a slimy, pink, ammonia-processed food additive in their hamburgers. The USDA actually approved the stuff. So if you would like to use the "job killer" argument blame the consumer.
The second is that pink slime serves a resource friendly and animal friendly purpose by using more of the cow. True, as far as the argument goes, but not eating beef is an even better way of conserving resources (the inefficiency of cattle as a food source is well documented). Likewise not killing the cow at all is a kinder act than making sure that every bit of cartilage and ligament winds up in the hamburger or hot dog..
My own preference, and there isn't any means of enforcing it except by increasing the availability of nutritional information, and knowledge of the process by which food gets to our table, is for people to eat real food rather than highly processed and highly engineered extruded "product".
As a start, I think everyone should read the book Fast Food Nation: The Dark Side of the All-American Meal, by Eric Schlosser. It goes into a great deal of detail on how factory farming and the fast food industry operates.
In Defense of Food: An Eater's Manifesto is another book with excellent descriptions of our descent from eating food to eating highly engineering food-like product. I think the bar should be set higher for what we consider acceptable eating habits. "It won't kill you", while a good criteria at the extreme end, is hardly an encouraging endorsement of any food or diet.