I've been wondering if wanting to be different that Will and Kate was part of it. Everyone keeps saying that they should look at how Will and Kate do it and follow their lead, but if they want to do it differently, having that example won't help at all. There are a few reasons I can imagine for wanting to be different.
First of all, as a lot of people have pointed out, Archie is not in the same position as the Windsor kids, so they could just think that it doesn't make sense to do the same thing as W&K are doing (and not have a good sense of what the best alternatives might be).
Second of all, there is the sibling relationship between Harry and Will that people have pointed out. That would be a very common thing.
Thirdly, even apart from the sibling relationship, I imagine that as first-time parents there can be some insecurity as to your skills as parents (which I think would be normal), which could drive a desire to make decisions yourself and maybe not listen to advice from some others to prove you are capable of doing it yourself (and this one could come from both Harry and Megan). If I was a first time mom, I probably wouldn't really want to hear everyone saying I should just do things exactly like my sister-in-law, even if I liked her a lot.