One important reason for this is that improvements in public transit tend to cost a lot of money. For example, any attempt to create or extend a light rail system in an urban area incurs costs for installing the rails (which often have to be put up on viaducts or down in tunnels) and for further rolling stock. All of this costs serious money.
A second major reason is freedom and convenience. Many people (particularly those in the US) like to be able to go where they want, when they want to. They do not like to be tied to the schedule of a bus or train or to the specific routes traveled by those forms of transit. This makes it less convenient for them to use transit and it limits their freedom of movement to some degree.
When put together, these reasons show clearly why public transit is not always popular. It costs money and limits people's freedom of movement. Many people are unwilling to pay for something that would be inconvenient for them to use.