A hub does not need an ASIC because it is not buffering frames, making a decision, and switching the frame out of the correct port. A hub simply is a repeater with a bunch of ports. It regenerates the actual signal on the wire.
A switch is a layer 2 device that makes a decision based on the layer 2 frame destination MAC address. The more ports you add to a switch the more processing a switch is doing. Just a few ports can be handled by software written to run on an off-the-shelf CPU. As the number of switch ports increase, the general purpose CPU using software solution can't keep up. The ASIC is basically a CPU that is not a general purpose CPU but is a CPU for making switching decisions very quickly. It can't be used for much else. This is similar to a high-end graphics card that has a special CPU for graphics processing that wouldn't be good for general applications. Hence the name, Application Specific Integrated Circuit.
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