Learn Russian: Я сам избегаю пауков.

The verb избегать (to avoid) requires its object to be in the Genitive case. This is a common pattern for Russian verbs that express fear, avoidance, or lacking, such as бояться (to fear). Even though you are directly taking action to avoid the spiders, the grammar rule for this specific verb dictates the Genitive case rather than the standard Accusative direct object.

Since паук is an animate noun, doesn't its plural Accusative form look exactly the same as the Genitive?

Yes, it looks identical! Because a spider is an animate noun, its Accusative plural form is exactly the same as its Genitive plural form (пауков). However, if you were avoiding an inanimate object, like conflicts (конфликты), you would clearly see the Genitive case at work since the forms wouldn't match: Я сам избегаю конфликтов.

What does the word сам add to the meaning here?

The pronoun сам means "myself" in this context and is used to add emphasis. It contrasts the speaker's own habit with someone else's, essentially saying "I know others might not mind them, but I myself avoid spiders." Because сам is in the masculine form, it tells us the speaker is male. A female speaker would say Я сама.

Why use the imperfective verb избегаю instead of the perfective?