I believe your professor is probably right in saying that Jesus used the word "synagogue" rather than "church" in Matthew 16:18.   However, he is creating a false dichotomy.  In other words, the distinction is of no significance.  Here is what I mean.  We can assume that when Jesus gave the discourse recorded in Matthew 16 he was speaking in Aramaic.  The Greek word translated as "church" in most English Bibles is ekklesia.  This is the word found in Greek manuscripts of Matthew 16:18.  The Greek word is directly translated as assembly or simply group gathered together.  Obvioiusly, ekklesia is not an Aramaic word.  Probably the closest word in Aramaic to the Greek word ekklesia is Synagogue (please be aware that I am no expert in Aramaic).  Therefore your professor is probably right that Jesus most likely actually said Synagogue not church.  Actually, more precisely, he probably said Synagogue, not ekklesia.    There are two reasons the point your professor is of no significance to the meaning of Jesus’ words.  First of all, we do not know what he said in Aramaic, but what we do know is that one eye-witness to the event felt the closest Greek translation of the Aramaic word Jesus used is ekklesia.  Second, as far as I know, the only reason your professor feels confident in claiming that Jesus used the word Synagogue is that this is the closest Aramaic/Hebrew word to what we have in the Greek Matthew 16:16!  In other words, he assumes this is what Jesus said because it is similar the the Greek ekklesia in our received text.  If he then proceeds to try to say that Jesus had a Jewish concept in mind (Synagogue) rather than assembly (ekklesia) , he is using circular reasoning.

I cannot rule out the possibility that there is some significance to this distinction your professor makes, but given the linguistic source (Greek) it is difficult or impossible to prove there is a distinction.

John Oakes, PhD