The fundamental issue with teaching intelligent design in public schools involves constitutional separation of church and state coupled with intelligent design's inability to be treated as a [dis]provable scientific theory and its direct relation to religion. Any theory, no matter its following or logic, is not considered good, in the scientific sense, if its basic hypothesis cannot be tested and retested in an attempt to [dis]prove it. On the other hand, evolution is able to fulfill these terms and has done so over the years in such a fashion that it has not been successfully disproved thus making it a valid scientific theory.
The religious relation to intelligent design and its inability to be treated as a proper scientific theory is why it does not belong in state/federally funded schools. Rather, it can be taught in appropriate settings such as at home, church or anywhere else that does not violate the constitution.
A quality example of a logical theory that cannot be tested is Talcott Parsons AGIL paradigm within sociology which is extremely intuitive, but completely untestable making its scientific use virtually nonexistent. At the time when Parsons created this paradigm Parsons realized there was no statistical method, yet invented, that could possibly test his theory. Because of this the theory created without regard to testablility. However, during Parsons lifetime the statistical power to test such a theory has been developed, rather than make the theory testable Parsons wrote an essay saying that his theory was so well logically devised that it need not be tested, merely accepted. The inability to test Parsons theory, despite its brilliance, is one reason why it is rarely used today in actual practice and is rather taught in classical theory courses as a background in sociological thought and growth.