Why won't my sims use these kitchen counters?

I would guess the mats as you seem to have used MOO for them. In addition, I noticed there are bushes on the other side of the window. Did you use MOO on them too? If so, they could be invading the 'space' where the counter is positioned. It might be worth checking MOO or not as sometimes leaves stick through the walls. I also tend to find some of the suspended lights can cause objects to become useable and as Galacticgal said test the cupboards too.