Help, I have a Passive Immunity question

I'm taking an immunology class and having a hard time finding out the answer to a homework question. I have scoured my textbook and the internet, and I'm not sure if my answer is correct. Can anyone help me?

Here's the question:
Why wouldn't you use serum from someone with immunity to a bacterial infection to protect another from the same type of infection?

My answer is that serum contains antibodies and would be considered passive immunity. Protection will typically only last a few weeks.

But, I'm not satisfied with that answer because it doesn't really explain why you wouldn't want to use it at all. I'm really stuck. Thanks.