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The answer to this question can be found in Book XXI. I cannot give you a page number because I do not know what edition of the book you might have.
The basic answer is that the bow is too valuable to Odysseus for him to want to bring it along to the war. It is valuable as a keepsake -- for sentimental reasons. This is because the bow was given to him as a token of friendship by a man named Iphistus. The bow had belonged to Iphistus' father who had been killed by Hercules. When Iphistus gave the bow to Odysseus, Odysseus was very honored and therefore, later, he did not want to bring such a special bow to war.
Here's a quote:
This bow, then, given him by Iphitus, had not been taken with
him by Ulysses when he sailed for Troy; he had used it so long
as he had been at home, but had left it behind as having been a
keepsake from a valued friend.
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