Neville didn't let the wand choose him because he used his father's wand. This could be why his spells didn't work so well. However, when the wand broke and he went to get a new one at Ollivander's, the wand chose him. He then becomes the leader of Dumbledore's Army, which is why this theory stands.
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Facts About Harry Potter
RandomFan of Harry Potter? This book will tell you facts that might have not even known. #61 in facts - 16 August 2018 #24 in goyle -24 August 2018 #529 in brave - 30 August 2018