So, hypothetically, of course...
You're amongst people you know. In the room, there are, among others, a young couple and their few-month-old baby. The baby has a good disposition and is generally the star in the room. Lots of 'oo'-ing and 'aa'-ing and you do a bit of "aww, isn't that sweet" yourself. Eventually, the baby gets offered up for holding. People clamor to hold the baby. Eventually, Young Parent turns to you, expectantly, and says "Would you like to hold the baby?"
Thoughts that come to mind:
This outfit isn't drool-resistant.
Why? I've been watching it for the last hour. It doesn't do much.
I'm fine without that responsibility, thanks.
and similarly (apparently) inappropriate things. It isn't that you have a problem with the baby, you just have no desire to hold it.
Question #1: Does this make you a mean or cold person?
Question #2: What do you say to Young Parent?
and, finally, Question #3: Is it rude to not hold the baby?