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Cooking is processing in the sense 'processing' is used for foods. I think the processed food focus isn't on processed foods being inherently bad but that buying food already processed is more likely to be bad for you. Theres probably plenty of processed foodstuffs that end up healthier than what you make with whole ingredients.

If removing the bran of the wheat makes the pasta processed, why doesn't removing the liver of the chicken do the same?

Because everyone removes the liver from a chicken, and only mad scientists remove bran from wheat.

To my knowledge, no one has a consistent definition as to what qualifies as ultra-processed, even yours there is a bit non-standard. We're pretty sure twinkies are ultra processed, but then there's questions on whether something like ground beef even with minimal/zero additives counts as processed or if we do add things to it, is it ultra-processed? Vegetable soup is probably pretty alright, but hey, it might qualify as 'ultra-processed', the qualifiers for it are a mess.

I agree with the sentiment they're going for, i.e., we probably shouldn't be eating twinkies as the cornerstone of our diet, but I wonder how these studies have shown how dangerous ultra-processed foods are when none of them seem to include a definition that you can consistently tie back to discrete items. It feels like we would all likely be better served by identifying the problematic elements (like the hydrogenated fats/etc) within the ultra-processed foods and focusing the conversation on those.

It is a little confusing

I wonder if you're overthinking things and/or perhaps mixing up concepts based on your questions.

What they are saying is that diets higher in processed foods, especially when a significant number of calories come from highly / ultra processed foods, tend to translate into people who are less healthy and have higher rates of chronic disease.

This isn't saying that all unprocessed foods are inherently healthier than all processed foods, nor is it an attempt to label every specific food item good or bad. The article even addresses that some of these labels (ex: ultraprocessed) are a bit nebulously defined.

Also, it's important to consider the reasons why certain types of processed foods are problematic, as the reason(s) can be different from product to product or even brand to brand. For instance, processing can destroy, neutralize, or even remove important nutrients (ex: vitamins and minerals). Processing may involve the addition of or concentration of salt, sugar, fats, preservatives, and other chemicals that can all contribute to chronic health issues. Some processed foods avoid or minimize these concerns, others seem to embrace them all like it's a competition.

Pasta is not one monolithic thing where all types and brands are the same. Some will be more or less processed than others. I'm surprised grapes would be confusing, if they're raw grapes they're unprocessed, if they're canned/jarred/preserved, then they're processed. I'm not sure what the tofu question has to do with anything, as this isn't about classifying each and every food item as good or bad. People do eat cooked chicken that doesn't have salt, oil, sugar, preservatives added. But even so, raw chicken is one of the ingredients in a lot of at home recipes. In the context of processing wheat into white flour for pasta, most/much of the vitamins and minerals are removed, and the carbohydrates (starches/sugars) are concentrated. It's not really equivalent to removing an organ from an animal. A closer, but not perfect analogy, would be removing those livers, then extracting only the oils/fats/lipids from them ... and then that liver oil would be more akin to a product like pasta or white flour.