Building up when you still have the capability to build outwards is resource intensive and wasteful. Not only do you have to consider the initial outlay, but you also have to manage resource movement and logistics for the entire tower. This is a nontrivial problem. Just look at the Burj Khalifa's plumbing and work out how much effort it takes to pump water that high.
If we're discounting high population density as a reason for doing this the only thing I can think of is to show off. Building a high city with amazing views and keeping swathes of unspoilt countryside around is a pretty powerful status symbol for the country that can do it, but it's fundamentally flawed in an economic sense.
Just for fun though: lets look at some potential reasons and why they aren't actually that good as justifications:
Spaceport access: Taller city = higher spaceport = easier to get to space, right? Nope. Not only do you still have to get the components/people/fuel up the skyscraper city in the first place, the height difference is only going to go a tiny way towards the energy needs for getting to space and, more importantly, getting up to orbital velocities
Reducing commute times: More compact city = shorter commute as you don't have to go as far, right? Nope. The elevator requirements for skyscrapers can be complex and might lead to people having to cross a whole floor to get to an elevator to take them up to the floor they need to be on to cross back across the floor to get to work.. phew
Efficiency: A'la Asimov's Caves of Steel series, it might seem to make sense to condense everything so you can process everything centrally and in the same way. Again: this doesn't work in reality, as the logistical concerns begin to outweigh any potential gains very quickly
Moving cities: This seems reasonable at first. Despite the fact that it essentially comes back to a question of high population density, it seems to make sense to put lots of floors on your moving city, however: If the city is ground based you have to worry about the centre of gravity and wind concerns, so it makes more sense to make a dome shaped or zigguratesque city (Similar to Mortal Engines). If you have an airborne city you want to spread the load as much as possible to get as many engines/zeppelins as you can, so a flatter city works better there. If you're in the ocean a decent depth of keel could improve the cities stability, but only if it's also strong enough to take the increased pressure on the lower levels and also the stresses involved in dealing with waves (I think this was a plot point about a floating hotel in a Dirk Pitt novel, but I can't remember which..). Finally: Spaceborne cities would be best off as spheres, even if you're accelerating the whole thing it's the best shape to reduce the various stresses while flying and also turning
Population control: Keep the populace close and in one building and you can lock them down. You also lock yourself in with them, and if a crazy cult decides to set fire to the lower floors you're utterly boned.
Essentially: The only reason to build an upward city that makes sense is if your population density is going up. This might be because of an increase in population, restrictions on where people can build, large draw for people to be near the city centre or reduction in available city size. Or if you want to brag to all the pretty girls about how big your municipality is.