No, it's not the parent's fault.
I've been a stay at home mom for 6 years, I've found that you should potty train when THE CHILD is ready. It makes it so much easier on everyone. Some kids take longer to be ready, and that's ok. My four year old son is Autistic and still wearing pullups around the clock. We're working on potty training, but at a very slow pace. He gets overwhelmed with the bathroom easily, and when he does he refuses to use it!
Good luck, mama! Take it easy on yourself! Your child will get it eventually! :)