@leocg it says Opera One, but I believe my problem is already solved now... please note the actual name of the option I said above so that people can be better helped when they have this issue please and thank you.

@Kriz1985 I believe I have found it... but it is not called, "throw away cookies upon exit," nor anything like that... it is called, "on-device site data." Which is probably why I missed it before... because every response to this problem says to look for, "throw away cookies on exit," and that is not what it is called at all... I believe that has fixed the problem... thanks.

@leocg I have, "Site Settings," when I search for Cookies, but there is no, "throw away cookies upon exit," option...

@leocg I do not have any, "siteData," option under Content...

@leocg I believe in it Opera One... I dunno it just says, "Opera Browser."

I am mad. Last time I came in here, mad about this, I got blocked from even using this site. Do not do that again.
Opera keeps logging me out of every site upon exit. Every response to others who had the same problem, it always tells them that they have selected an option called, "throw away cookies on exit." But I have scoured all the options in Opera's settings, and that option does not exist at all!! I dunno what they are talking about. Searching settings for, "cookies," does not show that option and I even went thro and read every option in settings and none of them say that... At all.
I don't have that setting... it doesn't exist for me. So I cannot turn it off, because that option doesn't even exist.