Since Trinitarians say it is wrong to use “God” and “Jesus” in a reciprocating proposition, why do they use “God the Son”?

Original Answer

You quote Wallace as follows:

For a genitive in simple apposition the two nouns are equivalent to a convertible proposition. Thus, “Paul the apostle” could be unpacked as “Paul is the apostle” or “the apostle is Paul.”

What Wallace is doing is making an argument from the Greek grammar. Your own logic is flawed because it takes his argument that relies on a particular Greek grammar and applies it indiscriminately to English usage.

In English, "Paul the apostle," is a reciprocating proposition no more than, "Paul the disciple," or, "Paul the human being," are. In English the meaning is ambiguous, but the latter cases are clearly not reciprocating propositions. "Francis the pope," is a reciprocating proposition, but, "Francis the Argentinian," is not.

The phrase, "God the Son," is obviously not a reciprocating proposition. The whole logic of that phrase is to clarify what is being talked about by narrowing the designation. It's like saying, "John F. Kennedy the younger." Adding, "the younger," specifies that we are talking about John F. Kennedy Jr. rather than John F. Kennedy Sr. Similarly, adding, "the Son," specifies that we are talking about the second person of the trinity rather than the Father or the Holy Spirit.

Admittedly trinitarian grammar can be difficult, but your idea that, "X the Y," 'unpacks' to, "X is the Y," is simply not true in English.

In order to make your case you would have to quote Greek sources--ideally conciliar--that contain the terms, "God the Father," and, "God the Son," and then show through grammar and context that a reciprocating proposition is intended. Instead what you've done is made an invalid argument from English.

Addressing Revisions

Thomas Pearne has made several revisions to try to make his argument valid:

[b] God the Son in Greek

The phrase "God the Son" is not found in the Bible, but is found in later Christian sources. By scribal error the term is in one medieval manuscript, MS No.1985, where Galatians 2:20 has "Son of God" changed to "God the Son".

This does not provide us with any Greek theological text that uses the terms in question (i.e. "God the Father," or, "God the Son").

[c] Wallace ExSyn 266–69 b. Is θεός in John 1:1c Definite? Although it is certainly possible grammatically to take θεός as a definite noun the evidence is not very compelling. The vast majority of definite anarthrous preverbal predicate nominatives are monadic, in genitive constructions, or are proper names, none of which is true here, diminishing the likelihood of a definite θεός in John 1:1c. Further, calling θεός in 1:1c definite is the same as saying that if it had followed the verb, it would have had the article. Thus it would be a convertible proposition with λογος (i.e., “the Word” = “God” and “God” = “the Word”). The problem with this argument is that the θεός in 1:1b is the Father. Thus to say that the θεός in1:1c is the same person is to say that “the Word was the Father.” This, as the older grammarians and exegetes pointed out, is embryonic Sabellianism or modalism.

Wallace is saying that θεός is not a definite noun and therefore does not represent a convertible proposition with λογος. This is exactly the opposite of what would make your argument valid. I'm guessing we would find a similar exegesis of post-Biblical, conciliar Greek texts.

In Greek "God the Son" is ho Theos ho huios (ὁ Θεός ὁ υἱός) and because both terms are definite like Wallace's example of modalism at John 1:1c the parallel is perfect.

You've given the Greek for "God (is) the Son," but you haven't shown us where to find it in a Christian theological text. Wallace denies that the reciprocating proposition occurs in Jn 1:1c. What you are saying is, "If this term appears--without contextual clarification--in a Greek theological text, then we would have to read a reciprocating proposition." Okay sure. Does it appear in a Greek theological text in that way? We have no evidence that it does. No parallel exists because you haven't produced a single example of "God the Son" in Greek theological discourse!