Can't break blocks with Swords

I was riding my horse, and I fell into a cave, I was wielding a sword, but I was in Creative Mode so I wanted to break the block above me so I could jump up with my horse, but as I tried to break the block, I noticed that I couldn't break it. So i tried with a few other blocks and it had the same result: It has the breaking effect like you are mining something, but the block simply doesn't break.