Yup.
We can't kill off the ecosystem one inconvenient species at a time.
Exactly. Agreed, the wolf could eat our cattle, but what about the Pyrenean ibex? The last one got killed in 2000. Was it threatening the pasturing of mountain cows, leaving the poor children of the local farmers without milk? Or did the male ibex just have a good looking pair of horns?
Advanced animals like most mammalian life are not purely instinct driven, but intelligent, feeling beings. Some are highly intelligent, approaching human levels.
Recent studies have proved wolves to be highly intelligent. Yet you just said they're pest, killing of which weren't wrong.