People seem to think that the Dunning-Kruger effect means "smart people think they're dumb and dumb people think they're smart!" but I don't think that's very accurate.
What they actually found was that lower-skilled people thought their skill level was somewhat higher, and higher-skilled people thought their skill level was a little lower, but not to the point where their relative perceived skill levels inverted. At no point along the skill curve did people incorrectly perceive themselves to be higher or lower in skill level in comparison others who were actually higher or lower in skill. The perceived skill curve was a little less steep than it should have been, that's all.
I think a more appropriate cognitive bias would be the curse of knowledge: https://en.wikipedia.org/wiki/Curse_of_knowledge