Why Peppers Are Sometimes Considered Fruit - Tasting Table
Briefly

Chefs and home cooks generally prefer to use the culinary classification, which regards peppers as vegetables and has more to do with how they taste.
The reason for a botanical classification of peppers is to help scientists identify different or new varieties, while the culinary definition is more about taste and practical use.
We generally tend to think of fruits as sweet or tart, which is why they are perfect in recipes for puddings, desserts, smoothies, and cocktails.
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