It could have been the delivery of the conversation, something like:
Hey <DAD>, <your partner> and i noticed your daughter loves our Dogs, since we work most days would you be comfortable with her helping out <your partner, and I> in the mornings or evenings? We are getting started on our family but our little helper will take a few years before we can put them to work.
Women are generally seen as less threatening, so having conversations where you drop your partners name and status in front of yours helps. Identifying yourself as a parent, or working to be a parent also can “soften” your male appearance. Finally, dont push, drop it and take no for an answer because some people are never going to be comfortable.
Also dont expect your words or message to be translated to adult, there have been times where our kids have said things that “they were told by an adult” and when we have called the school/daycare/friends parent, its often a misunderstanding where the kid has no idea what the context or specifics meant so they tried to convey their own version. So next time keep it short and sweet, and if possible immediate. “Are your parents around… Could I talk to your <DAD/MOM>… we need to get <DAD/MOM>s permission first”
A few things that have helped me in the past are being prepared. While my kids were in diapers or potty training I rolled everywhere with spare gear and I was quick to offer to other parents, especially at parks and public areas where people can be caught unprepared.
I had a situation in an airport where a Mom was overwhelmed trying to hold 1 kid, keep another in the stroller, and sign the doc’s to check her strollers and car seats. I was already in line, so I said “Im not going anywhere, can I help you with something or hold one of your kids?” She did an up and down check, realized I was in fact in line, and its an airport, so she handed me her baby and I stood where she could see me and rocked them while she finished what she had to do.
I would also suggest taking some child safety classes, I coach sports, and am a Den leader in our local Cub Scout Pack. Both programs required me to take classes regarding identifying child predators, unsafe situations, and child abuse and how to report them. Classes like these can help you see interactions from an outside risk perspective.