That doesn't sound like Humanism to me. That sounds like
scientism, which as a scientist, is a
massive peeve of mine. Rejecting all knowledge/thought that cannot be investigated with the scientific method is foolish and reveals a lack of understanding of the limits of that method (and of the sciences that study human nature). The role of science is to descriptively understand aspects of the universe that can be quantified and analyzed statistically. Some aspects of the universe can neither be easily quantified nor analyzed statistically. Such questions are inherently nonfalsifiable and beyond the scope of science (such as ethics). For some questions, asking for "evidence" is absurd and missing the point entirely.
I put evidence in quotes there, because this person that you're speaking with is defining evidence in a very limited manner. I see this often with adherents of scientism. They limit what constitutes "evidence" to that which would be acceptable to the scientific method. The irony is, nobody in day-to-day living holds to such rigid standards of evidence. We do not, for example, reply to our wife saying "I love you" with a "prove that to me scientifically or I won't believe you." We accept our personal experience as a valid form of anecdotal evidence that our wife loves us. It's much the same with religious/spiritual experience. Each type of evidence has its proper place, and I'll grant that anecdotal evidence is frequently misused. However, throwing it out wholesale as this "humanist" does is overdoing it.