They wanted to build just on a small stripe on the side of it, it is not as if they would have to fill the whole place with houses. But even that was shot down via "Volksentscheid".
I think the referendum against building in Tempelhof saw right through the project and understood what its end goal would have been: it would have created apartments that those being priced out of Berlin wouldn't have been able to afford. The losses would be socialized (namely, the park) while the benefits would go to the wealthy.
For those unfamiliar with the situation I found this article [1] which, biased as it is, I think accurately reflects the opinion of the common Berliner at the time. If the plan had proposed 100% social housing, I bet the story would have been different.
Honestly one of the things I like most about living in Berlin is the fact that local politics manage to represent the public good effectively. I'm a well paid tech worker, so I would be fine either way, but I'm happy that my neighbours who are hairdressers or hand workers can also enjoy a good quality of life here. I would hate for it to become a playground for the rich like London or Manhattan.
But that is nonsense - apartments are apartments, even if wealthy move into those apartments, it would free the apartments they previously lived in. Also, it would be money for the city.
Also it is not just social cases who have problems with high rents in Berlin. You suggest the majority of people in Berlin want only more social housing, implying most of them are social cases themselves?
I think most Berliners would read your comments as "it is a good thing that we give a part of our public park to the rich because they'll give us their less-desirable apartments in return. Like trickle-down economics, but for apartments". And if the current situation is any indication, those rich people will keep their old apartment and rent it, or sell it to foreign investors. Either way, say goodbye to ever owning a place in the city where you grew up.
As for the second part: Berliners feel that the city should belong to those that lived there when no one wanted to, and recognize that those people are probably not rich. Kicking the hairdresser that lived there for 40 years to make room for the tech bro is not generally seen as a positive development. Social housing would ensure that the city remains in the hands of its citizens.
The park would not be "given to the rich", presumably the parts open for building would have been sold to "the rich", with the money benefitting every Berlin citizen (ideally - but we know our government her is composed of very good people, right?).
Also what does it matter if the "rich" rent out their old apartment? What is needed is supply of apartments. Per supply and demand, more supply means lower prices.
Do the people expect to live in luxury apartments for little money?
And it is very touching that nobody wanted to live here 40 years ago and the people held on. But then they could have bought their living places for very little money. Also the whole place was subsidized by the USA as a stand against the Soviet Union. The people staying benefitted a lot.
There already is a construct for the place where you live belonging to you: it is called "buying your own place to live". If you choose to rent instead, you signal that you don't necessarily want to stay forever.