Worker being hostile and unprofessional at work ?

So we have a this guy at work who is part of the group, and has a tech lead role. Being a lead he always gets to assign tasks. But when he assigns them he always follows it up with 'this will only take me 2 minutes or 5 minutes' implying he would have got it done sooner and he is better than us. This happens all the time again and again. He constantly wants to show how superior he is to the rest of the group. If someone like me does better or sees a mistake he is very unprofessional in his tone and words. I am taking it as some sort of bullying. Cannot go to my manager because she is married to him.

So question I have is: 1. Am i wrong in considering this bullying. 2. What should i do about this ? What are my options ?

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