If you were adopted...and loved your adoptive mother and father...would you still want to know who gave you life? Or would you not want to know anything at all and let it all stay buried?
I'd be curious but otherwise it wouldn't be a driving ambition in my life to find out who they were. If you're happy and loved, what else is there? The Romans had similar attitudes toward adoption. An adopted son had every legal right that a biological child had, including rights of title, peerage, and inheritance. A biological son, an adopted son, there was no difference to them, none at all.
What if your birth mother/father tried to contact YOU? Would you still be curious? And what if, for example, your adoptive parents told you things not quite true. Would you be interested in hearing the other side of the story? Like, if they told you your mother/father was dead. Or in prison or something bad to keep you from searching or even speaking to her/him?