Telemachus and Penelope both occupy relatively lowly positions in ancient Greek society. Although Telemachus develops considerable maturity throughout the poem, as a relatively young man he still isn't strong enough to be able to take on his mother's suitors and expel them from his father's palace. For that, he will need the assistance of Odysseus. Hence the importance of setting off on his voyage to find his long-lost father.
As a woman in Greek society, Penelope is expected to be subservient to men. She doesn't like or admire any of the suitors, but she knows that at some point she'll have to give in and marry one of them. In the meantime, all she can do is stall them, using trickery to delay the dreaded hour when she will have to choose one of the suitors to be her new husband. But she too cannot remove the suitors from the palace; only Odysseus, with his physical strength and authority as king of Ithaca, can do that.