I think urban green space is great, as long as it also comes with housing density. The problem is excessive greenspace coupled with mandatory low-density single family dwellings. You end up creating more sprawl and more carbon emissions as the people who can't afford to live in the close-in suburbs sprawl outward.
Also, I say all of this as an environmentalist. Suburban parks do more to protect homeowner wealth than they do to protect our planet. Carbon emissions, ocean acidification, widespread habitat loss (think palm oil plantations in Borneo, not racoon territory in your backyard) are far more pressing environmental problems than suburban densification is by any stretch of the imagination.
Seeing a few trees torn down to make way for an apartment building is a very tangible loss of greenery, but it's ultimately better for the environment. Density allows people to be more efficient in their use of resources, and ultimately preserves more habitat for wildlife.
That's a great point, and one that has been largely missed here.
I used to live in a city with aggressive green-space initiatives. (85% of the city had to be green space.) Locals would tell me that it was "good for the environment".
I'm sorry, but no. Green space initiatives force sprawl. They're bad for the environment, full stop.