Homeowners and landlords don't want more building for exactly the same reason: They own property there and consequently want it to become more scarce so the price of their asset goes up at the expense of tenants and new homeowners.

In general the homeowners are more numerous but the landlords are somewhat more organized.

The homeowners are also being taken for a ride, because less restrictive zoning reduces the value of units (since you can increase the supply of them) while increasing the value of each piece of land (since you can now build more units on it). And the homeowners (and small landlords) are typically the ones with a high ratio of land to units, but they get hornswoggled into demanding the thing that really benefits the corporate landlords who own the existing high density buildings.

The typical homeowner hardly owns any land, though. They aren't going to see much benefit to themselves if high-density development happens near them.

It's not about whether it happens near them, it's about whether it's allowed to happen on their property, because then their property becomes worth more to a developer whenever they want to sell it, and anyone else who wants to buy it then has to outbid the developer.

Suppose housing units in some area are going for $600k but are currently limited to one unit per plot. That changes, now you can build up to 20 units per plot. A developer can build units for $100k/unit (their cost, not what they would charge you) plus whatever the property cost to begin with. In other words, they could pay you that $600k, spend another $1M constructing 10 new units there, and then sell them for $600k each, i.e. $6M from investing $1.6M. $12M on 2.6M if they build 20 units. What happens then?

They're going to start doing that whenever a house comes on the market, so over time the cost of a unit comes down, e.g. to $400k. But that's the price for the new units which are only consuming 5-10% as much land. Developers are selling those, not buying them. They want the land that doesn't already have a lot of units on it, i.e yours. And even at $400k, building 10 units gets them $4M from $1M + whatever they pay you. Which means whenever a unit like yours comes on the market, every developer is going to want it.

Even at the lower price per unit, and even if they had to pay you $1M for the land instead of the original $600k, the developers would still be making a tidy profit. And since they have to outbid each other when your house comes on the market, how much are they going to bid when not being the high bidder means not making anything?