Is it wrong that I don't feel like I should be expected to share personal information to resolve a conflict?
It depends on what type of information they want. Do you not want them to know more about you?
No. I care mostly about myself, so I'll keep my information private.
Wanting to keep your information private is reasonable and normal. However, if you can help resolve a conflict, you should consider whether sharing the requested information is that big of a deal. If you can help others, perhaps you should consider sharing some of your information that won't put you at risk.
I mean that I should keep my information secret to protect my privacy.
Oh yeah, I get that. You don't want sensitive information getting out that could put your financial life at risk. By all means keep that stuff private.