1. Because walking is always a good way to explore any city.
Think about it. There is only as much you can see from a car or a bus. Public transportation in Split isn't that bad, but it might be confusing for a foreigner who is also a first time visitor. Fortunately, most people speak decent English so you can always ask for help, but still you can't see everything from a bus. If you a tourist, strolling your day away has many benefits.
2. Because Split is very pedestrian friendly city.
Split is a very pedestrian friendly city. Honestly, I don't think you even need a car to explore Split city. Google map (or just grab a free map in the tourist office by the city's cathedral) will be enough for most people. If you find yourself lost, don't hesitate to ask for help/or directions. However, I don't think you have to worry about that. The city is really not that big, so getting lost is not likely.
3. Because it is …