malec, I think this varies based on the city you live in.
Among citizens of Dubai, if there is any objection by the general public to building tall towers, they would typically quote one of these reasons:
1. We don't need more expatriates coming in to live in these towers and mess up the demographics even more.
2. This is pointless and is just an ego trip and one of the signs of the nearness of the End of Times, as quoted by Gabriel in the Qudsi Hadith (second in importance after the Quran) in reference to barefoot bedouin shepherds of Arabia: "You will see the barefoot ones, the naked, the destitute, the shepherds and camelherds take pride in building tall structures in abundance."
3. Construction material is getting too expensive with the huge demand... we can't afford building homes anymore.
4. There's too much pollution with this construction, increased traffic and the build quality and finishing is poor.
5. I'm not interested in living in a tower, I want a garden and more privacy.
Generally though, residents are accepting of skyscrapers and they're used to them.
There are specific areas for them and people still get to keep their suburban villas and low-rise beach resorts, cafes and malls for middle class to rich (Jumeirah/Barsha), have a midrise area with all kinds of shops and restaurants for the poor and middle class (Bur Dubai/Deira), and a highrise district with restaurants/shops for the upper middle class and rich (Sheikh Zayed Rd/Dubai Marina).
Most skyscrapers on Sheikh Zayed Road have shops/restaurants at the base and it's very vibrant along each side in good weather (despite 10 lanes of a highway in the middle - a service road separates it).