Ok so based on your response and others, it seems like 1) raw is being compared to 2) non-microwave other cooking methods (say stove or oven) versus 3) microwaves, so three categories roughly of cooking (fair?). In the (2) non-microwave cooking category, concern has been raised about burning foods to a char (some raw food enthusiasts bring this point up I think):
(this article suggests microwaving instead of food getting burned, so take with a grain of salt): https://www.birmingham.ac.uk/research/perspective/does-burnt-food-give-you-cancer.aspx
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“the nutrients broke down”, which by the way, tends to happen when you cook stuff, microwave or not
I think this is a good point to highlight. This is what some (1) raw food enthusiasts argue for, against cooking with or without microwaves. They argue cooking can reduce the nutrients in food, so people should consume raw foods instead. It seems this point may be admitted, however people often argue for cooking food for the trade off of killing off certain diseases. So the counter-argument in favor of the raw position would be to emphasize cleanliness for most people (and then only possibly cook for "at risk" people), i.e. mostly eat raw unless you are likely to get sick from raw food.
In fact, studies show that due to the shorter length of time microwaves need to heat up food, they tend to damage the nutrients the least
This would be true if all else was equal, but it was being argued here that microwaves may uniquely cause damage over other methods of cooking.
Boiling vegetables also robs them of some of their nutritional value because the nutrients leach out into the cooking water.
Right, I saw one site arguing that it was correct that microwaves removed nutrients (Vitamin C) from broccoli, but that this was similar to how the stovetop might affect it
eating melted plastic
I think this is a good point to take note of, that even assuming microwaves to be safe for the sake of argument, some people may wrongly microwave things thinking them to be "microwave safe". So there may be dangers to microwaves beyond the act of microwaving itself, which I think would be good to note.
In a Swiss clinical study
I get that people are critiquing the studies, but it should be fair to at least consider it uncertain if microwaves are healthy or not; it sounds like people should avoid them when they can, but if they want to take the risk, that's for them to decide, and there should be discussions on if it is healthy or not.
For example, plants given microwaved water did not fare well. This study seems easily reproducible, and I am open to it being explained if it is not thought to be relevant, but I'm curious about your thoughts on it: https://www.giftofcuriosity.com/plants-microwaved-water/