They think it’s impossible for humans to age
Penelope basically tells the suitors that the man who can string the bow and shoot an arrow through 12 axe heads will win her hand and marriage. So disguised as a beggar Odysseus successfully strings the bow and grabs an arrow and shoots it straight through 12 axe heads. Eventually he makes his way back to Penelope but she isn’t convinced is really him. So she tells him that he can sleep outside her room on the bed on the bed that Odysseus carved. Oddysseus snapped and asked her who moved the his bed that was carved straight from the roots of a olive tree that the room was built around. Penelope knew that only he would have known about the bed so she instantly knew it was him.
