Engineer is a professional designation. It requires a BS, a series of exams, and years of work experience. Engineers are regulated by professional organizations. Unless you've gone through the training and the tests, you aren't an engineer. You're a developer.
That said, I strongly discourage software developers from using the term "engineering", mainly because I don't want the PE folks to start thinking they have any sort of business licensing software practitioners or getting involved in evaluating their competence.
As a math major (abet one with an MS in Industrial Engineering), I put no claim on engineering, and I dispute any claim engineering has over software. I think CS is more a branch of math than of engineering - so if the PE folks want to interfere in this, they can start by going back to college and taking a couple years of real analysis, abstract algebra, complex analysis, advanced linear algebra (with proofs, not some watered down "applications" course), and number theory. When they're ready to pass an in-depth exam on those subjects in order to get licensed to write code (after failing the first time), they'll have a taste of what regulatory capture really means.
It is, but designing software isn't CS any more than designing bridges is physics.
If you want a title to mirror your ability, choose one that refers to abilities. (And again, yes, due to hystorical reasons, those are rare. Want to start a trend?)