This is especially true of babies, especially if you're a guy. People, for reasons that aren't clear to me, love watching other people hold babies. Passing newborn babies around from person to person is a longstanding tradition that a lot of folks seem to really love, but the awkward man fears. If you don't want to hold one, I promise you, there is not a single combination of words you can string together to communicate this point to anyone.
You:"Oh, no, I really- Please, I'm sure I would drop it. Just everywhere."
Them:"Oh, nonsense, you're just nervous, you'll be fine, here it's easy!"
You:"No, thank you, I'm just not at all fond of babies."
Them:"Oh, you're so funny. Here just hold her, she won't bite."
You:"You don't know that!"
You:"Actually my whole family was killed by babies, and I swear to God if you hand me that child I will-"
Them:"Look, he likes you! He wikes his Uncle Danny, doesn't he?"
You:"For reasons that aren't clear but are probably related to my general life awkwardness, I am very uncomfortable in this situation, do not hand me your baby."
Them:"You're just shy, you'll be great at it"
"Look, he seems nice, but can I just put him somewhere? Does he have... like a drawer, or basket?"
Everyone always assumes you're shy, or embarrassed, or nervous, even though deep down you really want to hold that baby. But here's the truth: the socially awkward man genuinely has no affection for your child. Further, he is terrified that there are several unspoken baby rules and that he will break every single one of them. He'll hold its head in a way that makes babies blind, or it'll start crying because he accidentally pinched a nerve that only babies have, or he'll make a face that scars her for the rest of her life.
None of this goes away when the children get older, either. Being around someone else's child at any age is confusing, because there is always a different set of rules and the lingering fear that you will have an impact on this child's life, which is terrifying because you are so, so dumb. The socially awkward can barely navigate their own life, and suddenly they're face-to-face with a four-year-old that's peed itself and there's no one else around. The child complains about pants-wetting and all you can think to say is "Look, this is clearly a situation but I'm not- I don't really know what my jurisdiction is, legally, when it comes to, like, your pants. You're not my property and I have no interest in your future. Please go somewhere until this issue resolves itself."
"Just keep your head down, and believe in yourself, and be far away from me."
Little children recognize no boundaries and feel no shame, and those two things define the socially awkward human.
Socially awkward guys don't want anything to do with a baby or child based on the very understandable fear that they will somehow do it wrong, (and also because babies aren't interesting). Not everyone sees a baby and thinks "That's so precious I need to hold it now, but how do I ask?" Some guys just see a baby and think "You are a baby."
Please don't make him hold your baby. Just let him sit quietly in the corner, mentally complaining about his haircut and wondering how everyone else learned how to dance when he didn't.
Check out Dan's look at 5 Things They Never Told Us from last week or The 8 Most Awkward Sexual Moments in Comic Book History.