I'll bite the bullet:
How can I have a conversation with him about this?
Easy: you don't. It's simple:
It's almost never a good idea for non-parents to give parenting advice
As an experienced parent myself (I have lots of children), I don't even give parenting advice to my friends unless asked. There have been plenty of times I've wanted to, and plenty of times where I thought a little friendly advice could help, but I know that more often than not it will backfire badly. I've had non-parents give me parenting advice before. I'm too polite to literally laugh people out of the room, but that's usually what I want to do. The advice has never even been remotely applicable. That's the case here too because:
Parenting is complicated. Sometimes you don't know what you don't know, and in my experience that is what is going on here. "Don't spank your children" seems like simple and actionable advice, but it really isn't, and as a non-parent I don't think you appreciate how complicated this is. In particular:
A) Spanking is a method for enforcing boundaries. You can't always just remove it
Boundaries, rules, and structure are very important to children. Don't get me wrong - I'm not voting for children to be raised in army boot camps, but it is important for parents to set boundaries and rules. It both keeps children physically safe and is also an important part of how they learn to interact with the world around them and grow into mature adults.
Imagine parents who use spanking as a regular tool to enforce boundaries for their children. If you take that away without providing an alternative, the result could easily become children without boundaries. A common source of frustration for parents is feeling like they have no control over their children. Taking away a primary tool for that without giving the tools to replace it is (IMO) more likely to make matters worse than better. All that to say:
B) Even if the general goal is good, that doesn't mean that giving advice is helpful
We had a mom and her 3 year old daughter staying with us for a bit. It was clear that the child in question liked doing things her way (which meant ignoring her mother), and the mom didn't really know how to handle it and primarily got frustrated as a result. It seemed to me that the main problem was that the mother was unsure how to properly enforce boundaries. For a 3 year old (IMO), judicious use of spanking can be a good way of dealing with this. However, I never gave advice to the mother, and never suggested spanking, regardless of whether or not the mom was willing to hear advice from me (she probably would have). I kept quiet because:
- I didn't know the daughter well enough to know if spanking would have actually been something she responded well too
- I didn't know the mother well enough to know if spanking was something she could actually execute appropriately
- I knew that the advice by itself would be meaningless - this was not a small change and what was really required was a new approach to parenting. That might involve spanking, that might not, but I knew enough to know that I couldn't give the mother the guidance she needed. What was needed was not a simple conversation where I convince her to do something different, but more of a "parenting mentor" that could help her come to a better place all together.
I think these general points are all very applicable to you:
- You don't know anything about parenting in the first place - you just have one "fact" (spanking is bad) that you are taking as "Truth"
- You don't really know anything about how your brother spanks his child
- You don't know anything about how your brother parents or what methods of discipline work best for his child
- As a result, you don't know if this "fact" of yours is actually going to be helpful to your brother and - more importantly - you don't know how to turn it into actual advice that will be helpful.
In essence, you are treating parenting as a list of "do's and dont's". It's not. Every child is different, and it is the job of every parent to get to know their particular child and figure out how to guide them best. You have neither the experience nor proximity to help your brother navigate this issue. Any attempt to do so is unlikely to be well received, but more importantly you are probably more likely to hurt his parenting than help it.
On a controversial note
It's probably obvious from above, but I think your fears about spanking are overblown. Obviously spanking is growing out-of-style these days, and some professional organizations recommend against it (studies about how spanking has negative impacts on child psychology are also popular). However, even that doesn't mean this is the hill you should choose to die on, even ignoring everything else I've said above. Some estimates suggest that upwards of 85% of children are spanked during childhood. That includes you, your brother, and myself. When something is that common it is hard for me to seriously consider the possibility that any amount of it might have immediate and lifelong negative repercussions, which seems to be your concern.
Anecdotally, I've been around lots of kids and I'd loosely group their parents' parenting style into three categories:
- Parents who set and enforce clear boundaries, with or without spanking
- Parents who don't discipline their children at all
- Parents who abuse their children and use spanking as a cover.
Not surprisingly the latter doesn't go well. Item #2 (parent's who just don't enforce boundaries) doesn't actually go much better. However, when it comes to item #1 (i.e. good parents), I've never seen a big difference between children who are spanked and children who aren't.
In summary: Nothing you have said suggests that your brother is harming his child. Both because of your lack of experience, and because you are not in a close relationship with him, it is unlikely that your advice will be well received. Moreover, because of your distance and inexperience, you can't do anything but repeat what you have heard from others, and you are not going to be able to give actual, practical help. As a result, just don't do it.