I was answering the question that I think they needed to be asking, not the way it was written. If you’ve ever made an earring (and I suspect you have) then you know what I am talking about.
They want to make an earring, you can’t remove nodes from paths that don’t overlap to some degree. Your method merely makes them one path object, it’s not really useful.
We didn’t get into actually making a hole in the upper circle which is probably the next question. (hint, place a small circle inside the upper circle and do path->difference, or if you are feeling particularly clever, use stroke to do it with stroke to path, but here I go again, trying to be helpful when I should apparently stick to the question at hand.)
I get annoyed when people reply to what I consider closed topics, too… but in this case, you may have answered the question as written but didn’t really answer the spirit of what is being attempted, so I thought my reply could help.