When Lady Catherine says the family should have gone to London every year for the sake of the girls' education, Lizzy says her mother would not have objected but her father hates London. I am assuming it wasn't possible to send Mrs. Bennet and the girls alone, maybe for financial reasons or reasons of propriety. So his dislike of the city deprives the girls of social opportunities as well as the chance to learn from superior teachers. Perhaps Mary would have learned some taste to go with her musical execution, and perhaps the younger girls would have been better suited for society. The Gardiners were kind enough to rescue Lizzy and Jane, but they could hardly have been expected to take all 5 girls under their wing when they have their own children to think of.