Why did they say "Il ne veux pas DE glace" instead of "Il ne veux pas UNE glace"? In the translation, they said 'He doesn't want an ice-cream', not 'He doesn't want ice-cream'.
You can say “ il ne veut pas UNE glace “ - but in French this will be taken to mean “ he doesn’t want ONE ice cream “ (so how many does he want). Translations are not always direct and literal. In English we might say “ he doesn’t want an/any ice cream” or even just “ he doesn’t want ice cream” - in French they would all be ‘’il ne veut pas de glace”.
As Maarten has mentioned, when the verb (vouloir in this case) is negated the "de" takes the sense of "any" so "Il ne veux pas de (any) glace" becomes "He doesn't want any ice cream"
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