penelope didn't have to turn the tree bed into a riddle. she could have asked odysseus to prove his identity, to tell her something only he would know — which she actually did a few books earlier, when she asked the beggar to describe odysseus, and odysseus told her about a purple cloak with a particular golden brooch that she fastened herself twenty years ago. when penelope tells telemachus they have signs by which they'll know each other, you sort of expect more of the same. and instead, she decides to trap him. like a bug in a cup.
and it's delightful to me, idk, how odysseus has been trapped and cornered in various way throughout the odyssey, but arguably never so that he has to tell the truth to get out. (with the phaeacians, maybe? the omniscient narrator corroborates some of what he tells them, but do we really know everything?) and in fact he is not trying to get free of penelope. he wants something from her, wants to convince her, wants to be welcomed home, but until this point he's lied to her, revealed himself to other people before her, and been distant with her (though also patient! he doesn't try to strongarm or rush her into accepting him; it's his idea to sleep elsewhere).
except penelope isn't looking for him to be distant and patient. penelope lies in a way that requires odysseus to stop playing along — not only to prove that he knows what odysseus knows, but that he's willing to tell the truth about himself.
