Not your keys, not your bitcoin. It's not a meme. Well, it is a meme, but it's a mean based on facts.
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Discussion
The deeper concern is there are many actors who discourage holding your own keys and even incentivize not doing so.
it makes absolutely zero sense to hold bitcoin on an exchange. unless you're waiting to get to a million sats or so before you withdraw, i don't see any other viable reasons.