What does "linear" mean to you? Integration is linear[1]. The Hilbert space of all the functions you care about is linear[2]. Life is locally linear[3]. So maybe "non-linear" is just a red herring.

1. https://en.wikipedia.org/wiki/Linearity_of_integration

2. Not really but close enough.

3. I don't know what I mean either, but https://en.wikipedia.org/wiki/Linear_time-invariant_theory is interesting anyway.