I believe it's because he was quite attached to his old wand and didn't really want the power and stigma that came with the elder wand. I don't think it was destroyed either, I don't even think it can be destroyed. I can't remember where but I thought he placed it somewhere where it would stay until he died leaving it without an owner.
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The strongest wand in the Harry Potter series is the Elder Wand.
it is one of the three deathly hallows (The Elder Wand, The Stone of Ressurection, and The Cloak of Invisibility.)
Wands choose their owners and no wand is weak simply through its own properties. A wand would be weak because the owner wasn't a very capable witch or wizard. Vincent Crabbe and Gregory Goyle were the worst students in Harry's year at Hogwarts.
Dumbledore was the master of Elder Wand until he was disarmed by Draco Malfoy at the Astronomy Tower. Malfoy himself did not know that he was the true master of Elder Wand. In part 7 when Harry, Hermoine and Ron were captured by snatchers and brought to Malfoy Tower Harry Potter disarmed Draco and becoming the master of Elder Wand. So, Harry Potter remained the true master of Elder Wand in the end.
right when voldomort gets the elder wand