You can think of virulent as full of poison, and poison of the fast kind. Not a slow stain that shows up months later, but something that gets into a body and does harm almost at once. From that one picture the word travels in two directions: it stays in the body, where it describes a or a venom that is unusually strong; and it moves into language, where a person's hatred behaves the same way — deep, fast, and meant to hurt.
From the word’s history
From Middle English virulent, borrowed from Latin virulentus 'poisonous', from virus 'poison, venom' plus the suffix -ulentus 'abounding in, full of' — literally 'full of poison', which is exactly the picture both modern senses use.
來自拉丁文 vīrulentus（有毒的）：vīrus 是「毒液」，-ulentus 是「充滿…的」，字面就是「滿是毒」。今天的兩個用法都還踩在這個字面畫面上。
Wiktionary, "virulent"
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