You are implying a number of questions that have dependent, but distinct answers:
1. Why can't rafters be sechach?
Although on a Torah level rafters are valid sechach, the sages prohibited using "nesarim" (manufactured wood planks) which are thicker than 4 hand-breadths, suspecting people may see no reason to sit in a sukkah if their own home's roof is constructed in the same way. This is codified in Shulchan Aruch O.C. 629:18.
The S.A. also brings a custom not to use nesarim which are smaller than 4 hand-breadths. The Mishna Berurah 49 explains this is for one of two reasons:
a. This may cause people to build their nesarim schach in a way that doesn't let the rain in
b. People started building their roofs out of planks smaller than 4 hand-breadths, so these would also be included in the original prohibition of nesarim.
2.Why can you fasten the rafters with, or rest the rafters on metal or plastic, but cannot do so with the schach?
The Shulchan Aruch 629:7 questions whether one may place a wood ladder on the sukkah and place more schach on top. While many interpret this as questioning whether a ladder is considered kosher schach, there is an opinion (that we try to keep) that there may be an problem supporting schach with a material that is invalid for schach. So while supporting schach with metal or plastic does not invalidate the sukkah, we try not to do so (MB 22).
However, as we see from S.A. O.C. 629:8, there is no issue of using invalid schach materials to support the supporters.
3. What amount of rafters will invalidate a sukkah:
According to reasoning "a" in the first question, you will not invalidate the sukkah as long as the rafters are less than 4 hand-breadths.
According to reasoning "b", the rafters will be considered invalid schach. Those laws require a different question.