If you have trouble abandoning your house, usually for buying a new one, then you are probably just accessing your housing panel from the wrong place.
If you access your housing panel from the button on the mini-map, you will not get the option to abandon house, only to pay fees and manage permissions.
Instead do this:
1.Press C to get to character panel
2.Choose housing panel in the bottom left
3. Now you get a new panel with your house and maybe kinship home. To the left of maintenance is the abandon button.