Questions & Answers about Я ничего не имею против этого плана.
This lesson teaches 'напротив' (opposite), but this sentence uses 'против' (against). How are they related?
They are closely related! While напротив is used for physical location (opposite or across from), the root word против is used for conceptual opposition, like being against an idea, team, or plan. Just like the prepositions in your current lesson, против always requires the Genitive case.
Why does the sentence use 'этого плана' instead of 'этот план'?
Because the preposition против forces the following noun phrase into the Genitive case. План is a masculine noun ending in a consonant, so it takes the Genitive ending -а to become плана. The demonstrative word этот (this) must match its noun, changing to its Genitive form, этого.
Why are there two negatives (ничего and не) right next to each other?
Russian strictly requires double negation. When you use a negative pronoun like ничего (nothing), you must also negate the verb with не (not). You cannot just say я ничего имею; you must literally say 'I nothing not have'.
Is я ничего не имею против a common way to say 'I don't mind' in everyday speech?
Yes, it is a very common and natural set phrase meaning 'I have nothing against it' or 'I don't mind'. In casual conversation, you will also frequently hear it shortened to just я не против (I am not against it).