Software Engineering is closer to Computer Science than to actual Engineering. It does involve some engineering problems and solutions, but overall, it mostly is programming. Even if you check university courses, the CS and SE content are pretty much the same with little differences between them.

Many software developers/programmers call themselves "engineers" as they seem to see themselves on the same level as real Engineers. In my opinion, this stems from their feelings of class inferiority and a belief that since they make similar levels of income to engineers and make complex "things" that they are deserving of the title. To me, this is the purest expression of wanting to be labor aristocrats.

They are not engineers because:

1. They do not design things that human life/safety is dependent on. Yes, there are some software applications in medical and other fields that do, but generally the vast majority of these people are not "designing" things of that nature. On that note
2. There are no hard set principles or rules that developers must follow to uphold the first point. Yes, there are some guidelines that they generally follow, but compared to real Engineers, it's most a free for all. And on that note...
3. Real Engineers must be cognizant of consequences of the failure of their designs at all times. There are strict bodies that regulate design and to even become an Engineer, you must have guidance and approval of other Engineers to be considered someone who can work independently. If a bridge falls because of poor Engineering, the Engineer and their firm will face consequences and can have their licenses revoked. Yes, some developers have been sued for shoddy coding or breach of contract, but this doesn't stop them from continuing to work in the field beyond simply having a poor reputation.

In Canada, the regulator of Alberta recently ruled that software developers are not engineers. Not that the bougie govt of Alberta is good in any way, it makes my point. It's mostly just classism. And no, I'm not a developer or an engineer and nor are my family. So you if you see someone claiming to be a "Software Engineer" or similar, they're really just a grifter. You might as well just call gardeners "plant engineers", novelists "writing engineers", or painters "art engineers".