There are two major arguments for incorporation. First, you can argue that the 14th Amendment clearly applies the Bill of Rights to the states when it says that states cannot take away their citizens' liberties without the due process of law. The liberties they cannot take away are the liberties enumerated in the Bill of Rights. Second, you can argue that it is simply a matter of justice. If it is unjust for the federal government to infringe on your right of free speech, it must surely be unjust for a state government to do so.
Both of these arguments have their critics. As to the first point, critics point out that the authors of the 14th Amendment did not specifically say that the Bill of Rights should apply to the states. They could have said so and did not. As to the second point, there are those who would prefer the fundamental fairness doctrine. This doctrine would be more just because it would force the states not just to adhere to the Bill of Rights, but to be fair to their people in all important ways.