The phrase "destructive tendencies" refers to harmful behaviors or actions that can cause damage or create negative outcomes. It means someone or something has a inclination or habit of causing destruction, harm, or damage.
Though these dogs are not overly active, they are highly people - oriented and may develop destructive tendencies if left alone for too long. (pawster.com)
Separation anxiety is, in many cases, the root cause of behaviors such as excessive barking, inappropriate elimination, and other destructive tendencies. (1800petmeds.com)
This can lead to destructive tendencies if your Pit mix is left alone for long periods of time. (thehappypuppysite.com)