i've only registered a new account to tell you that you shouldn't be stubborn when someone more experienced try to give you an advice, even when it's ill mannered or not phrased in the most kind way, nevertheless, they're absolutely right
in the screenshot, you're clearly using md5, go ahead and look up those hashs, ex. the second one, "68b74872368d6742ecb24537351de526" that's "letmego123"
with bad security awareness, your best bet is best practices, you're currently using PHP/5.2.6, are you aware how many exploits there is to compromise the users table on your precious db? check for yourself (not talking about anything advanced, a skid can get that done)
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if there is anything i learned being on this form for years, it's that it's always better to go learn and study instead of arguing; also it's okay not to know about something, but it's never okay to push people away when they try to help/criticize you, you're on epvp, not defending your phd :).
edit: to make this more helpful, you can simply generate new random password, hash it and send it to the user email, all it takes is literally 2 google searches.
generate random password:
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send email in php:
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i swear, i've junior developers at my company who only use snippets from stack over flow and get paid for it :')