This can actually happen quite often, although it is much more likely for Ones to think of themselves as Eights than the other way around. You’ll see why in a moment.
Ones and Eights don’t just share the same Group*, but also quite a few similar looking behaviors: Strong-willed decision making, action-oriented ways of living and, most of all, a strong sensibility for justice.
That last point however shows most clearly how Ones and Eights are fundamentally different: Ones see justice as a moral principle that needs to be upheld, and they think a lot about how to treat everyone fairly and equally – that’s why they make such great judges, attorneys and reformers: They are great at coming up with the logically irrefutable argument why their position is the morally correct one.
Eights on the other hand don’t think much about justice as an abstract principle, they just can’t stand seeing the weak being bullied in the streets. They rarely think in general terms about justice for everyone, but in concrete terms: Protecting their family, their friends, their tribe, not by convincing them with the morally correct argument, but through sheer force of will.
This is why some Ones want to identify themselves as Eights, because they would like to have the Eight’s natural authority and aggressiveness. It’s not that Ones can’t make great leaders, but the truly aggressive type – the one that dominates by pure strength, not through having the moral high-ground – is reserved to Eights.
* If you don’t know about Groups yet, you can learn about them here. The basic idea is that of the nine types, three groups of three types each have overarching commonalities. Type One, Type Eight and Type Nine are one of those, called the Body Group. Their common theme is a strong connection to the body and the instinctive side of us – hence the “gut feeling”.