In Homer’s Odysseus, Odysseus leaves his son Telemachus and wife Penelope, and stays away from them for almost twenty years. Telemachus determinedly searches for his father. In Odysseus’ absence, his house gets attacked by a large number of suitors who are after Penelope. So when Odysseus reveals his identity to Telemachus finally (in Book 16), they make a plan to take hold of their place and kill Penelope’s suitors. Telemachus informs Odysseus that there are more than one hundred suitors and, hence, Odysseus makes a careful and smart plan to accomplish this task.
Now, therefore, return home early to-morrow morning, and go about among the suitors as before. Later on the swineherd will bring me to the city disguised as a miserable old beggar
As per the plan, both of them have to return to the home separately next day. Telemachus has to secretly go to the palace first, and watch the suitors in Odysseus’ absence. He is also supposed to take hold of their arms. After sometime, Odysseus will arrive at the palace disguised as a beggar to engage the suitors. According to the plan, when Odysseus will finally reach, both of them will do a surprise attack on the suitors.
The answer to this question can be found in Book 17, which is when Telemachus tells his swineherd to lead his father into the city so that he might beg food there and receive shelter why he goes straight to his mother to let her know that he is alright and to support her in her continued struggle against the suitors that she is trying to resist. Note what Telemachus says to his father at the beginning of this book:
Father, I verily am going to the city, that my mother may see me, for, methinks, she will not cease from woeful wailing and tearful lamentation until she sees my very self.
This of course suits Odysseus very well as he is able to make his own way to the city as and when he wants to, and arriving by himself and not with Telemachus will mean he will not attract attention and nobody will suspect his true identity. Thus Odysseus and Telemachus arrive separately because it helps Odysseus greatly in order to keep his identity concealed and to give him extra time to scope out the situation and enter the town in an inconspicuous way.