Heh. That was pretty much exactly my experience with my nieces.
I don’t dislike babies, I can even find them cute. But I’m also not all that into them. I won’t refuse to hold them, but I’ll pretty much never ask to do so.
Word. My grandson, who is at 9 months The Most Perfect Baby Ever™, came to visit from Germany. He’d been sick for a few weeks. They arrived by Military Transport int he midde of the night at BWI, and we drove them north to Philly. This baby landed with a respectable 102.2º fever and a thick ugly cough.
First, Philly. I got sick, my Dearly Beloved got sick, my brother got sick, my 79 year-old Mom got desperately sick. 
Then he went to Pittsburgh. Where my Ex-Wife got sick, my adult daughter got sick, and her cousin got sick.
Boy howdy, talk about yer vector. He was carrying the Teutonic Plague !!!
I would actually be more worried the other way around, that the baby might catch something from me. Is that at all a valid concern, or am I really no more filthy with disease than anything else in the baby’s environment?
kid is just testing your level of admiration.
Relevant Link! Be sure to click for the bonus panels! 
Snerk.
Okay, so about 17 years ago, I went to visit my cousin, his wife, and their child. He wasn’t an infant, but less than a year old. And I’m there, and my cousin says, “Would you like to hold him? Here” and puts him in my arms. And poof, I have a baby in my lap. And he says the same thing about wanting to hold a puppy or kitten but not a baby.
And yes, I am afraid of breaking it.
There’s such a thing as a friendly lizard? Who knew?
" do you want to hold my baby?"
" no, but do you happen to have a pet lizard?"
How about baby lizards?
My go to response to being asked if I want to hold the baby is “No, those things are contagious” sure enough my wife holds one of my sisters kids and BAM she’s pregnant. Now I just wonder if your immune to your own kid.
Previous baby-holding grumbles at:
http://boards.straightdope.com/sdmb/showthread.php?p=17281665#post17281665
I loathe babies, they are concentrated adult humans–every bit as nasty and selfish.
I am a misanthrope.
My revulsion to the offer of holding babby (and being touched in general) is so visceral and profound that people often think it’s an act and laugh ‘with’ me about it. And then hug me for the adorable jokester the believe me to be. Fools.
“Suffer the little children to come unto me, so that I may reject them with extreme prejudice.”
I don’t mind holding babies that are old enough to amuse me. If they’ve started grasping and smiling, and we can play pull-my-finger, that works for me. Little babies that just lay there with their head going in fifteen directions, I’m just waiting for my mom to come out of the woodwork saying, “Change your brother’s diaper!” That kills the mood for me.
Sounds like my pediatric rotation during med school (I got sick twice over an 8-week period).
Very young babies (weeks to a couple of months old) are relatively protected based on passive transfer of antibodies from their mothers before birth. This protection lasts even longer if the baby is breast-fed.
As the passive immunity wanes, babies are at increasing risk of contracting infections from others (especially germy toddlers and other children, who bring home delightful pathogens from day care and school).
It’s always good to know I am not the only one who does not find little babies cute.
Yes, I’m afraid of breaking it. Not to mention that I know how to hold a kitten or puppy. If it gets squigglywiggly, I know how firm I can hold it so it won’t fall on the floor. I know what to do if it starts barfing/peeing/pooping. You can’t just suddenly hold a new baby by the belly over the floor so the output stays off you. You can’t scruff a new baby and hold the legs so it doesn’t wiggle out of your lap. Babies are much more important than puppies or kittens, and much more fragile.
So yeah, babies scare the crap out of me and I don’t want to hold one. Give me a toddler any day. They are totally awesome.
My stand by response for when someone wants me to hold a baby is to blow my nose (I have allergies, so my nose always need to be blown) and say that maybe I shouldn’t because I don’t want the baby to catch whatever it is that I have. By the time they are toddlers, they usually need their noses wiped too…so all is good.
One time at my old job, we had an emergency meeting, and one of my coworkers couldn’t get a babysitter on such short notice, so she brought the kid in to work. It was…a baby, dunno how old. Not self-mobile yet. Anyway, I got in early, waiting in the conference room, then she and the kid arrived. She had to use the ladies room, asked me to take care of the kid while she did.
Panic.
OK, their necks are weak, right? And they’re born without skulls, or something like that. Put the kid in a sitting position on the conference table, one hand on its back, fingers supporting the neck, the other hand on its chest with a two-finger “V” holding its chin so the head didn’t fall off frontwards.
At arm’s length.
After about two minutes of this, some of my coworkers who were mommies arrived and freaked out.
“What? It’s safe, right?”
They took over the snuggly duties til mom got back.
And I never got asked again.
A little Catsup, few pickles, lots of cheese.
YUM!
I’m not a misanthrope, and I’m willing to hold your baby for a few minutes if you need me to because you need to go to the bathroom or put something away, or some such.
What I’m not froggy with is people who insist that I hold their baby because ZOMG11!!11! CUTEST. BEBBEH. EVAR!1!!! I know I was a royal pain in the ass on the SDMB after I had the sprog, and for that I heartily apologize. I now understand that you love your baby more than anyone else in the world, and that’s normal and natural. (I’m using the universal “you”, not the specific “you”.) I, on the other hand, do not share those feelings. I like babies just fine. I just find their parents to be insufferable.
I have zero problem with people who don’t feel comfortable holding babies, or who just don’t like them.
I do have a problem with people who think that “I like babies” is the correct way to express “I like doing to a baby things that would get me punched if I tried them on anybody bigger”. I also have a problem with people who won’t take “no” for an answer: whether you’re trying to get someone to try perfume, give you a hug, give money to your favorite cause or hold your baby, “no” should be understood as meaning “no”, rather than “come badger me some more”.