It's not something I have previously given any indepth thought to before, and I of course don't know the statistics of exactly how those relationships affect the family. i'll give you an answer though, based on my own subjective experiences as to why I think I would object at a personal level without further information.
1. In raising my son, I found there is a unique bond between mother and son. I know that he would be devestated as a little boy, and even now to see his mom with another man.
Fair enough, though this isn't really much different from other socially accepted practices, like divorce and remarriage.
Also, I think this might be an issue of conditioning: a child raised to expect one thing will be stressed if something else occurs. By itself, this doesn't mean that either thing is bad in its own right.
2. I think living out a relationship like that in front of my daughters would lead to excessive promiscuity in their future relationships.
Why is this bad, necessarily? And how do you define "excessive" in this context?
3. I think that such a relationship would undermine their father, diminishing him in the eyes of all my children.
Why would that necessarily be the case?
4. I would not want to pay child support for a child from another relationship.
I don't think the law would require your husband to support a child that isn't his, but regardless, this is a risk that you would be in a very good position to mitigate yourself.
5. I think the other woman would be hurt because she would always be playing second fiddle to me
So? Maybe she's got a "first fiddle" of her own back home and isn't looking for another.
6. I wouldn't want to risk sexual diseases.
Fair point, but this is another risk that can be mitigated.
And technically, there's a risk of you catching an STD even by sleeping with your husband, even if he's entitrely faithful (though I think it's impossible to know with certainty whether someone actually is entirely faithful, so that question is a separate risk you're willing to live with, apparently). It's happened more than once that a person can get a disease by non-sexual means (e.g. bad blood transfusion, contact with bodily fluids of an infected person) and then pass it to a partner through intercourse.
Any difference in risk between an open marriage and a closed marriage is only one of degree.
Also, in some ways, an open marriage actually decreases risk in this department: if a person in a closed marriage gets an STD through an affair, he or she may be reluctant to change his or her sexual behaviour at home to avoid the spouse finding out about the affair (even though it puts the spouse at increased risk).
I mean, if your spouse said to you, "honey, we can't have sex for a few weeks because I just got diagnosed with chlamydia and the antibiotics need time to do their thing. Oh - and you should go get tested for it, too," I'm guessing that your next question would be something like "how the (bleep) did
you get chlamidya?!"... right?
Anticipating a negative reaction might lead a spouse to never broach the subject at all, and continue in the couple's normal (and now unsafe) sexual routine and the spouse never to get tested until he or she starts displaying symptoms.
OTOH, an open marriage can, potentially, allow for better communication in these sorts of cases, which can reduce the risk to the non-infected spouse.
7. My marriage is a partnership, emotionally, and finacially as we operate a business together. There is no room for a third party.
If you're not into an open marriage for yourself, that's fine... I'm not sure I'd be interested in it for myself, either. But I do note that many businesses have more than two partners.