Programmers are essentially a type of translator. They translate constraints expressed in human language to constraints expressed as computer language.
At the higher levels you have more say how exactly that happens in terms of system topology, but at that point you're no longer just a programmer, but an architect.
Nothing is 'wrong' with it. You just do it at the detriment of your own career.
Even an idiot can put two and two together and conclude that if their business value depends on programs, then programmers create business value.
However the "software engineer" title is also applied to a lot of untrained programmers, so I'm not saying that this term is analogous to "dentist" even if it should be.
That’s literally it.
Nothing is wrong with it. Donald Knuth proudly describes himself as a programmer.
But a good chunk of the people reading this comment probably make more money than he does, and title inflation is part of the stupid game we have to play to earn outsized rewards.
So proceed with caution.
-- Ken Thompson, in his 1983 Turing Award lecture, "Reflections on Trusting Trust".