A great example I have seen showing processed vs non-processed foods is to simply put the food in a bowl of water. A lot of processed food will within a matter of minutes puff up to a multiple of their size, and when stirred will simply break up into a liquid solution. Natural (unprocessed, even minimally processed) foods will generally stay together for a lot longer.
That's not exactly a surprising observation. Same thing is true of most particleboard vs. unprocessed wood as well. You've failed to demonstrate at all why this would be a problem. Try your test on some chicken flesh compared to an identical piece of chicken flesh that's been chewed, swallowed, then chemically processed by enzymes and stomach acids in a human stomach. After you've tried that test, you may understand why your argument is easily dismissed by most people when you put it that way.
That said, there are reasons more heavily processed foods may be worse for you than unprocessed. One of those reasons is that the processed foods often simply come from poorer base materials than the unprocessed foods, which is why they needed to be processed in the first place. If the unprocessed food is a nice cut of chicken breast and the processed food is ground up chicken cartilage with a little bone and other otherwise less than usable bits of the chicken after everything is else is stripped off, then the processed food typically won't be as good. That's not universally true though. The hydroxyl-apatite in ground bone can actually be an ideal source of bio-available calcium, for example, and various organ meats which people typically shun in low-processed form are full of great nutrition. The majority of what goes into the processed chicken patty, however, is crap. Figuratively and also, to some degree, literally. Processes get developed to extract the maximum nutrition from food. This should be a good thing in a hungry world. Unfortunately, it's a hungry world with marketing departments and a heavy profit motive.
Processing of food isn't inherently evil. People have been processing food to extract more nutrition from it for millennia. Grinding bones to make your bread (bone cakes are full of calcium and nutritious bone marrow) is just one example. Another set of great examples are demonstrated by Pellagra and Kwashiorkor which are two medical conditions. You may not have heard of Pellagra, but just think of a typical portrayal of leprosy and you won't go far wrong. Kwashiorkor you have probably seen in ads for hunger-relief charities: swollen ankles, distended belly, hair loss, loss of teeth, dermatitis. These conditions are specialized forms of malnutrition that can occur in individuals who may actually be getting enough food to survive (although they may frequently be generally malnourished as well), but are suffering from niacin or protein deficiencies. They both tend to show up among people who live essentially exclusively on corn (poor Italian peasants in the case of Pellagra, and mostly African children living on food aid for Kwashiorkor). The all-corn diet might be providing enough calories, but is deficient in some vital nutrients. As it turns out, South American natives living on the same diet weren't suffering from these same issues. The reason comes down to food processing. Traditional preparation of corn involves nixtamalizing it, which basically means boiling it in a lime (the mineral, not the fruit) solution. The resulting processed food, called nixtamal is more nutritious (technically, it has fewer calories, but it provides a wider variety of nutrients) and people using it as a staple food are less likely to develop extreme nutritional disorders.
Going back to the downsides of processing food, there's the issue of preservation. Some processing, of course, preserves much of the nutritive value of the food for a very long time. Examples of this are salting, dehydrating and pickling. The processing does, however, often destroy some of the nutrients in the food as well and it typically involves preservatives that can be harmful when taken to excess (such as salts) or possibly preservatives that are harmful no matter the amount. Certainly any process that grinds up a food increases its surface area and potentially exposes it to rapid oxidation among other potential issues. Killing a food that's technically still alive can certainly destroy nutritional value. On the other hand, living foods stay alive by eating themselves, so you may lose nutritional value that way if you don't kill the food somehow.
The problem is, it's all very situation dependant. If you don't want to put in the huge effort of careful evaluation of every food you can form simple rules like: "processed food = bad", which can serve you pretty well. The problem you will run into is when you try to explain the universal truth of these simple rules to people and they demand a bit more than a simple heuristic.