Learn Polish: Krytykując społeczeństwo, uczeń odrzuca tradycję. - By criticizing society, the student rejects tradition.

While the -ąc ending (contemporary adverbial participle) normally shows two actions happening at the same time ("while criticizing"), here it takes on an explanatory or causal role. It translates better as "by criticizing" or "because he criticizes." It explains how or why the student rejects tradition.

Is it possible to use krytykując if a teacher is doing the criticizing, but the student is the one rejecting tradition?

No. A strict rule for using the -ąc participle in Polish is that the subject of the participle and the subject of the main verb must be the exact same person or thing. The uczeń must be the one doing both the criticizing and the rejecting.

Both społeczeństwo and tradycję are direct objects. Why does only tradycję change its ending?

Both nouns are actually in the accusative case here! Tradycja is a feminine noun, so its accusative form takes the -ę ending to become tradycję. Społeczeństwo is a neuter noun, and neuter nouns always look exactly the same in the accusative case as they do in the nominative case.

Can we form an -ąc participle from a perfective verb if the criticism was a one-time, completed event?