Family Echo doesn't allow you to delete someone that would result in leaving you with two unconnected trees (or a broken off branch). Before you can delete someone, that person cannot have any ancestors or descendents (children), so you have to delete those first. And if any of them have ancestors or children, you have to delete those first too. It becomes recursive, where to delete someone, you may have to first delete 10, 20, 100,... people before you're allowed to delete that person, depending on how filled out your tree is around that person.
Think first about why you want to delete someone. Is it because you got their name wrong? If so, then just change the person's name. You really should only need to delete someone if that someone never existed, e.g. you added a child but were mistaken and that person never had that child. If you've already added that child and perhaps their partner and children and grand children (and the partner's parents and siblings). Before you can delete that original child, you must first delete their children, then the partner's siblings, and finally their parents (and any possibly higher-up ancestors), and finally that partner; THEN you can delete that person.
In the case of duplicates, you can click "Change or delete" in the sidebar, then "Change Parents", then at the pulldown for "Set the mother" and "Set the father", click the current name (you may need to wait a few seconds for a list of names to appear after clicking), then scroll all the way to the top and select the blank line. Do this for both parents. Now you should be able to delete that instance of the duplicate person.