The Peshitta is most likely a composite of the Alexandrian and Byzantine text-types for Syriac-speaking Christians, much like how Jerome synthesized various Greek manuscripts for the Latin tongue. This would explain why the Peshitta agrees with the Byzantine text in some parts, while favoring the Alexandrian in others.
One could argue that the Peshitta is the original New Testament, and therefore the common source of the Alexandrian and Byzantine text-types and their divergence from each other, but that would ignore the weight of historical and manuscript evidence which favors a Greek origin for the New Testament.
Despite not being the original, the Peshitta can be useful for New Testament scholarship. For example, since the Peshitta is one of the oldest translations of the New Testament, it provides an early witness for the original text, much like how the Septuagint, though a Greek translation, provides an early witness for the Old Testament.
A more complicated argument would be that the Peshitta, in its very language, sheds light on the intended meaning of the New Testament. The Syriac of the Peshitta is a dialect of Aramaic, the language which Jesus and the Apostles spoke. Though the New Testament authors wrote in Greek, they thought and spoke in Aramaic. Since Greek was not their first language, they could have made linguistic errors in their writing, which the translators of the Peshitta may have corrected.
Imagine if an English-speaking student in Spanish class confused the words "nosotros" and "vosotros" because of their similarity in pronunciation and that they differ in only one letter. "Vosotros" is the plural for "you" while "nosotros" means "we" and therefore, if one were to confuse these words for each other, the opposite of the intended meaning would be conveyed. However, the Spanish student couldn't really be blamed if he didn't know any better. The Spanish teacher, in having a mastery of both the Spanish and English languages, would be able to correct his error.
Given that there is very little historical and manuscript evidence to support Aramaic primacy, if any, Aramaic primacists are forced to focus the majority of their attention to the apparent mistranslations within the Greek text, that only the Peshitta could supposedly correct.
Aramaic primacists suggest that in some places where the Greek New Testament reads awkwardly, that it may stem from a mistaken translation from an originally Aramaic source.
An example frequently cited is Romans 5:6-8. The Greek, translated to English, reads:
6 For while we were yet weak, at the right time Christ died for the ungodly. 7 For one will hardly die for a righteous (ÃŽÂ´ÃŽÂ¹ÃŽÂºÃŽÂ±ÃŽÂ¹ÃŽÂ¿Ãâ€š) man; though perhaps for the good (ÃŽÂ±ÃŽÂ³ÃŽÂ±ÃŽÂ¸ÃŽÂ¿Ãâ€š) man someone would dare even to die. 8 But God commends his own love toward us, in that while we were yet sinners, Christ died for us.
Aramaic primacists argue that the progression of the author's argument does not follow logically, in that the author claims that Jesus of Nazereth died for the "ungodly" rather than for the "righteous," so the author's statement that "one will hardly die for a righteous man" seems to be out of place given the paradox of "[God's ] own love towards us."
It is suggested that this reading lies within an Aramaic source. In Romans 5:7 of the Peshitta, where the Greek reads "righteous," we find the Aramaic word for "wicked" (Ã—Â¨Ã—Â©Ã—â„¢Ã—Â¢Ã—Â) rather the word for "righteous" (Ã—Â¨Ã—Â©Ã—â„¢Ã—Â Ã—Â) as expected. Furthermore, Aramaic primacists point out that in several Aramaic writing systems, contemporary to the times of Paul, the words "wicked" and "righteous" look confusingly similar. This leaves the implication that a scribe while translating, whatever the source of the discourse was, from Aramaic to Greek could have simply misread the word.
Polysemy ("split words")
"Split words" some Aramaic primacists treat as a distinctive subsection of mistranslations. Sometimes it appears that a word in Aramaic with two (or more) distinct and different meanings appears to have been interpreted in the wrong sense, or even translated both ways in different documents.
Perhaps the most well known example that Aramaic primacists cite is the parable of the "camel (ÃŽÂºÃŽÂ±ÃŽÂ¼ÃŽÂ·ÃŽÂ»ÃŽÂ¿Ãâ€š) through the eye of a needle." (Mark 10:25, Matthew 19:24, Luke 18:25) In Aramaic, the word for "camel" (Ã—â€™Ã—Å¾Ã—Å“Ã—Â) is spelled identically to the word for "rope" (Ã—â€™Ã—Å¾Ã—Å“Ã—Â), suggesting that the correct phrase was "rope through the eye of a needle," making the hyperbole more symmetrical.http://en.wikipedia.org/wiki/Aramaic_primacy
There are many more examples of apparent mistranslation that Aramaic primacists provide, without realizing that that their position of Aramaic primacy isn't the only possible explanation. If the New Testament were originally written in poor Greek, or at least Greek that is incorrect in certain parts, by men who spoke and thought in Aramaic, the translators for the Peshitta could have served as a much needed corrective. This theory may be false, but at least it serves as a middleground between those who believe in Peshitta primacy, and those who find the Peshitta to not be all that important for ascertaining the real meaning of the New Testament.