In edit mode is outline green or yellow? It must be green for furniture to be interactable and IIRC this particular house has a problem with placing furniture
To add to Narinhe's suggestion, place the furniture on different surfaces/different locations to see if the same issue occurs, and enable the option to prevent it from going through the floor (I can't remember the exact verbiage of the option at the moment, sorry); scroll wheel to ensure your chair is on the floor and not too far high or low.
I have this issue with other sittable furniture in the same home. I have three small stools set out in one area, two of them you can sit on and the third you can't. I have checked the one that you can't sit on and it has the green outline when placed.
A few weeks ago after the Markath update I noticed that I couldn't sit on anything in my home, that seems to have largely been sorted, but there's still at least this one, I haven't checked all the chairs to see if any others are affected.