If I understand you question correctly, you want to delete someone you have incorrectly added as partner and not keep two people on the family tree, just without them being in a current relationship?
In the first case, "splitting" means that by deleting the spouse in question, other members of their family would lose their connection to the tree. So, if you wanted to delete "Abraham", and Abraham has parents "Sarah" and "Isaac", deleting him would mean that Sarah and Isaac wouldn't be connected to the other people on the tree (same would go if you had children or partners of Abraham that are only connected to him and no one else). To delete Abraham, you need to delete everyone who is connected to him and no one else beforehand, then you can delete him.