I have to wonder to what extent that's actually true. To begin with, if you have a single family home in an area with high demand, upzoning could make someone willing to pay you even more than the house is currently worth because they could still turn a profit when turning it into ten or twenty times as much housing on the same lot. In other words, the value of the house may go down but the value of the land goes up when you can build more housing on it.
On top of that, higher housing prices don't necessarily equate to a better life or even more money. If your house is worth more but you still need a place to live then you can't sell it, unless you are planning to sell it soon in which case upzoning gets you more money because developers start bidding on your house before the new housing the upzoning allows to be built is on the market yet.
If not, it's not just your house that costs more. The other ones do too, which increases cost of living. Local shops have to pay higher rents and pass on that cost to you, or can't find local workers because young people can't afford local rent, so they have to close down. Then you get higher local unemployment and more crime and homelessness. You might even lose your own job because your employer moved out. What do you think drives offshoring? High domestic costs.
And if people are only thinking about the first order effect then they might imagine downzoning is to their advantage when it isn't. Which makes them support it but only until someone shows them the math.