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Trapping animals for fur coats is cruel.
Literal
Fur [possessive-の] coat [for-のために] animal [object-を] trap [with-で] capture [nominalizer-の] [topic-は] cruel thing is.
~のために here is the purposive 'for the sake of, in order to obtain' — distinct from the causal ~のために ('because of'). 罠で捕獲する ('to capture with a trap') uses the instrumental で. The whole activity-phrase is nominalized by の to serve as the topic, and the predicate 残酷なことだ ('is a cruel thing') delivers the moral judgement. こと after a na-adjective pack the judgement in abstract-noun form.