You're saying that a belief that has near total consensus among the experts is "simply false". You clearly haven't examined the evidence on rent control, and are simply making assumptions to avoid having to contend with the possibility that your preconceived notion is wrong.
>>Why do you think there's so much resistance in Europe towards market based rents if they think it will actually lower their rents?
1. Because economics is a difficult subject to understand, made all the more difficult by the multitude of special interests who need to discredit economics in order to rationalize the anti-free-market impositions that provide them with rent-seeking opportunities like subsidies and artificially suppressed rent.
2. Because people who already have rent-controlled units in high-demand cities don't want to give up their privilege for the benefit of the people of the nation at large, who, by virtue of rent control starving the housing sector of the capital to build more units in those cities, miss out on the opportunity to find a unit in the high-demand cities.
>>Should people be thrown out of their apartment they've lived in their whole life just because the property owner can find someone wealthier that's willing to pay more?
YES! They're renters. If they want the stability of not having to ever worry about housing costs increasing, they need to buy their own units. They can't rent, and then expect the stability of being an owner.
We need to be giving housing in the highest-in-demand localities to the people who can make the best use of it economically, which would be those who are willing and able to pay the most for it.
We also need to be giving investors the incentive to invest in new housing in these highest-in-demand localities so that more people can live in them, and that requires allowing rental rates to reflect the supply/demand dynamics. This is basic economics.