Besides the Obvious Reason
I'm certain that, eventually, Barney and Robin will come to terms with one important issue: kids. I'm not sure when: it could crop up within the next few episodes, or be left unresolved until their wedding day (which might be the reason why Robin is freaking out on that day, I'm not sure). I used to read all about upcoming episodes so I knew what to expect, but this year I've decided to avoid that to avoid spoilers; so maybe some article somewhere in the internet-verse confirms when the issue will come up and you might know, dear reader, but I do not. But, when it comes up is not the topic of this post today.
I'm talking about the issue itself. Now I know many of you, as soon as you read the title, have already concluded that it's because Robin's infertile. I know that, and it confirms that Barney and Robin will never have kids. But as a matter of interest, I want to ignore that fact and find more reasons why Barney and Robin are not parenting material.