What do microwaves do to you?
Source: I am an electrical engineer that has worked with in both laser spectroscopy and microwave radar.
They can heat you. There are several mechanisms for this. The main mechanism is ohmic losses, where free carriers are vibrated at the same frequency as the incoming radiation and due to interactions with the carrier's environment, give up its motion as heat.
In some cases, there can be resonances, especially in the gas phase. These are rotational resonances. For a rigid rotor with a moment of interia I, the energy levels are given by E=J(J+1) hbar^2 / 2I, where J is the total angular momentum quantum number. Because of decoherence, this ends up as heat as well. This is probably not an important mechanism in liquid and solid media like the human body, but there are absorption bands in the microwave region in the atmosphere for water vapor, for example.
One thing you can get are dimensional resonances. That is, the shape of a particular structure might be resonant at a particular frequency and enhance the absorption. Veritasium made a cool video about this I recommend:
At any rate, the dielectric constant of human tissue is quite high, on the order of 20-80 depending on the tissue type, and also very lossy, so the wavelength is much smaller in human tissue so that dimensional effects can potentially become important even for structures much smaller than the free space wavelength.
The power used in modern handsets is on the order of 10 to 300 mW, that is 10 to 24 dBm. This is a very small amount of power. Now it is true that with a short wavelength more of this will be absorbed near the surface. For example, the military has constructed a 94 GHz microwave area denial system that is intended to disperse crowds by heating skin. You can definitely feel this. It is unlikely that even if a handset was placed next to you and transmitting at 300 mW you would be able to tell. Since it takes 4.2 J to raise 1 g of water by 1 C, 300 mW would raise 1 g of water by 0.07 C/sec. A person weights a lot more than a gram, and heat conduction and convection would probably prevent any significant heat build up anyways.
Now if you had really strong fields, like those in a microwave oven, you can get dielectric breakdown. You can get effects like ionic and avalanche conduction in plasmas. For example, placing a candle in a microwave oven:
But the fields radiated by handsets are nowhere near the field strength needed to do this. But it's cool to watch in the microwave.
Real Engineering did a great video about 5G as well recently:
I don't think I will convince anyone using facts and stuff, but you gotta try.