Why do we not consider Nathaniel (John 1:49) as the first disciple to recognize Jesus as Messiah and Son of God but instead consider Peter to be based on his statement (Matthew 16:16)?
When you ask why “we” do this, it is important to note it is actually Jesus who does this. At some level we will have to wait and ask Jesus why he responded with great solemnity to St. Peter, and yet seems little more than amused with what St. Bartholomew (Nathaniel) says. That said, permit the following provisional answer to your question.
At one level, the two responses do seem similar. But in analyzing the texts we must first notice some linguistic differences. Nathaniel refers to Jesus as the “King of Israel,” whereas Peter calls him “the Christ.” And though some scripture scholars think that first century Jews would have used these terms interchangeably, they are nevertheless not identical. The term “Christ” (Greek for Messiah) is more theologically precise.
Secondly, we must remember that context is important. Nathaniel makes his comment as an early and almost ecstatic claim. Peter however makes his declaration after Jesus has spent time teaching and leading the apostles. And though the Father inspires his utterance, it is also rooted in the formation he has received from Jesus.
Further, there may be many other factors that are unknown to us simply in reading a written text. For example, there may be significance in the tone of voice, or the look on the face of Peter or Nathaniel that adds shades of meaning. There may also have been discussions or events prior to the utterances that influence the moments.
We can only trust that the Lord Jesus not only experienced all of these contextual things, but also knew the mind and heart of those who spoke. And thus he reacts one way to Nathaniel, and in a more solemn way to Peter.
At times, this is the best that we can do. Biblical texts supply us with what we need to know, not necessarily everything we want to know.
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