I basically agree with Lady Elanor's main point: there should be a reason for what your villain does other than "that's what the plot needed," and it should be a reason we can basically understand---whether or not the reason, or even most of the villain's actions, is ever revealed.
On the other hand, both as a reader and a writer I think it's important to not make a villain (as opposed to a mere antagonist with conflicting but non-malevolent goals) too relatable. Ideally aim for a characterization your readers will see as closer to "there but for the grace of God go I" than to "I'd want to be like that"
Making a villain that is relatable in this sense could contribute to greater popularity (for example much of the early popularity of the Star Wars series may have been down to Darth Vader), but as fiction always communicates some message we should do what we can to avoid making wickedness seem admirable.(And I'm hesitant to endorse Lady Elanor's reasoning leading up to her point; based on my understanding of the Scriptural account of human nature, villains become villains when circumstances reveal their innate wickedness---not that it's necessarily any worse than anyone else's before it has the opportunity to manifest---and then that wickedness compounds. But I digress, and that tangent would be better discussed in the Theology room.
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