Based on my knowledge of geology, adding to @sjuan76's answer:
- The geological map linked by Sjuan76 shows that most of the area underneath Chicago city is, as he says, beach ridges, sands, and gravel. These are extremely porous materials.
- The quote SJuan76 references indicates a very low elevation and constant drainage problems.
These two factors mean that the water table is at or very slightly below the land surface - which in turn means that building a subway would require constant pumping during construction to prevent tunnels flooding, and watertight construction techniques.
This combination, especially at the time the elevated lines were built, would have made an underground system prohibitively expensive compared to an elevated system.
Also, according to the Chicago L history site, the early lines were built by private organizations, where the provision of the sewer system and raising of city buildings was handled by the city authorities.
Even though the raising project occurred prior to the first elevated line, SJuan76's link makes it clear that buildings were typically raised between 3 and 6 feet - not nearly enough to support a rail tunnel. That link also states that the infill material was soil, so the water table would have remained at or near its prior level, ensuring that any underground system would be plagued with drainage problems.
All the other cities referenced are low-lying, adjacent to major bodies of water (in the case of St Louis, the Mississippi), and rest primarily on soil, sand, and gravel. These cities would have the same issues with an underground system vs. an elevated system.