Odysseus, disguised as the beggar, attempts a few thwarts of this question. At first, he just allows Penelope to tell her story and background which she hopes would help him begin to tell his own story. Fortunately for him, it gave him time to connect to something she said. Obviously he cannot tell the truth, he needs to keep his identity a secret to even her until the suitors are killed. But, he did think long enough to craft a story about the fact that he had run across Odysseus in his travels. This mention of her husband distracts her enough that she doesn't really ask for his background again. He describes Odysseus and tells of his safety. This confirms for her that he is telling truth because he knew details the common person would not just know about Odysseus, and then he gave her hope. He didn't have a good reason for not answering her questions, he just skirted them thinking as a beggar he could be considered a man of little importance.