Why do cities build high rise buildings?

There are several reasons. One is that in most cities, real estate prices are very, very expensive, and it is hard to buy a large lot in the middle of the city, so you often need to build up, rather than out, in order to have enough room.

Another is that there is a higher demand for space, so if you build more space (by constructing tall buildings), you can make a lot of money from renting that space to others.