"He is telling me that his real estate agent told him that he can use section 1031 so that no gains are recognized on the sale of his first house."

Did he operate it for rental, after building and before selling?

For future reference, a 1031 exchange intermediary is basically an escrow agent for handling the exchange properly, so that your client does not violate the rules. They don't replace the real estate agent, and a real estate agent is not, by definition, a Qualified Intermediary for a sale, since they represent the seller. There's a time restriction, too.

https://atlas1031.com/basics/what-is-a-qualified-intermediary/

Your client is in the construction business. The invested costs are inventory asset, until sold; not expense.