I agree that if you've labeled your software incorrectly as open source and you've been corrected, it should be re-labeled and the problem shouldn't be ignored. I will say, though, that personally I feel "free" software has a labelling problem. I'm not heavily engaged in the open-source movement, and a lot of the terms and wording and licensing confuses me to the point where I don't want to use it because I'm not sur…
You don't need to even choose a licence. That only comes in to play if you concern yourself with downstream users that care about licensing.
It really only becomes complicated when you want to release it and _also_ monetise it or restrict its use.
Licenses exist because of how this is ultimately at odds with how software actually works - it's basically legal DRM.
(I think licensing has valid uses in the current environment, but it's worth keeping in mind how absurd it is as a concept, it's basically a massive hack).