Object, noun clause, complement

Dear All:

I need your comments.

Someone (A) asked on another website for English learners about the grammar of this sentence, "He kept saying that he loved me."

I suggested the that-clause (that he loved me) is a noun/nominal clause, the object of "saying," and a complement clause.

Another person (B) objected to me, saying that the that-clause cannot act as an object and a complement in the meantime.

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I explained to B that, with another sentence "He is a teacher," "a teacher" is the object and the subject complement.

B doesn't concur with me on "a teacher" being the object of "is."

What do you reckon?