Having pets (dogs, cats, hamsters, etc...) in the house with small children?

My husband and I were wondering, in your opinion what are the pros and cons of having pets in a house with small children? pets such as hamsters, dogs, cats, ect... Our opinions differ slightly: Being raised on a rescue farm, my father had me around all sorts of farm animals from a very young age, even as... show more My husband and I were wondering, in your opinion
what are the pros and cons of having pets in a house with small children?
pets such as hamsters, dogs, cats, ect...

Our opinions differ slightly:

Being raised on a rescue farm, my father had me around all sorts of farm animals from a very young age, even as a toddler
As soon as I could walk, I was following my father around the barn watching him and helping with what I was able to help with...whether that was fetching water or holding a can of feed while he checked the hen's nests for eggs...
Of course I was supervised with the chickens and the dogs and other all other animals until I was old enough to understand that I needed to wash my hands after touching them; I also was supervised in handling of the animals and only allowed to handle them in an age appropriate manner
And as a result I'd like to think that I grew up more responsible, more compassionate as a result

My husband on the other hand had a very limited number of pets growing up, most of which were not in his care even when he grew older
However, as married adults, we share and love our fur-babies; we have 4 hamsters and one cat, all of which he plays with and cares for just as much as I do. I often catch him sitting in the play-pen with one fur-ball or another when I wake up in the middle of the night.
Man, he loves those little fluffies!
But at the same time he worries that having pets around small children might be a problem. He worries that having furry pets, like a dog or a cat might make our child more prone to asthma. Or that a pet like a hamster might carry some disease and transfer it to our child...

Now, I feel that if properly monitored that keeping pets would be beneficial to a child. The extra dirt around might even help boost their immune system (you don't expose them to things like germs when they are young, they are more likely to have a poor immune system as they grow older).
He worries that having pets around will make them ill.
We do however agree that pets would be an excellent way of teaching responsiblity and compassion...
We also feel that having pets is a good way of teaching about death, (its how my dad did it).

so whats your opinion?
what are the pros and cons of pet ownership for parents of small children?
including health risks/benefits and emotional risks/benefits?

(just to clarify, we're not fighting, just trying to find a comprimise and curious as to what other parents opinions might be)
Update: should probably also mention, we're pregnant right now; due in January
Update 2: also forgot to mention,
I've been working with the Humane Society for most of my life, since my father owns a rescue; I also have worked as a professional groomer and am currently taking courses to become a veterinary technician (graduate in 3 years) so proper animal care would not be an issue
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