It's showing you the public keys, not the private ones. Your should always keep your private keys in a safe place. The privates can't be derived from the public keys ;)
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They are internally being used and are public for everyone. With your public key one can validate the signatures of your operations and see if your account has been used for signing them. Nobody knows your private keys. They are nowhere stored but can be derived from your master password. For security reasons you should always login on Steemit or similar Steem platforms with your private posting key ;)
Take a look at some of the articles by @noisy on this topic, to better understand how this all works. I would suggest you start here:
https://steemit.com/security/@noisy/public-and-private-keys-how-they-are-used-by-steem-making-all-of-these-possible-you-can-find-answer-here