This conclusion is far from inexorable.
There are kinds of making other than engineering. Carpentry is not engineering. Cooking is not engineering. Gardening is not engineering. Sewing is not engineering.
All of these things involve making artefacts for users other than their designers, within a social context no less. All of them require specialist knowledge and tools, involve the application of judgment learned from years of experience, and give rise to communities of practice which codify their agreed knowledge in books. They even have formal certifications.
Before you can declare that making software is (or can be) engineering, you have to be able to explain why those things aren't.
My tentative theory is that engineering has rigorous ways to check whether a design will work before it is manufactured, and even before it is drawn in detail. A civil engineer can use known formulae to check if a bridge span of given dimensions is even possible before sitting down to design it. A chemical engineer can use known formula to check if a reaction is plausible. A mechanical engineer might need to draw a detailed design, but can then check it rigorously with finite element methods. When we make software, in practice, we have to construct the software and test the artefact, hoping that our tests are adequate. We can't do meaningful checks on the design itself, let alone on any sketch which prefigures the design.