I've seen this question come up before and I have an intuitive explanation: In circular motion, the object is being pulled toward the center, so some of its velocity is being imparted from its tangential path toward the center. If its position with reference towards the center is changing, meaning if its continuously being pulled from its tangential path, then the tangential velocity is always increasing, but this increase is never seen. Its like if an object is moving in a straight line and some of its motion starts to be imparted towards the side: in order to maintain the same speed in the original direction it would have to be accelerating in that direction; this is what I meant when I said it is not seen. Just to take an extreme example for purposes of clarity: suppose we move back and forth in a straight line; in order to move in the opposite direction, we must stop, then accelerate. if we take the limit over shorter and shorter time intervals and over shorter and shorter distances, then this back and forth motion will approach a point where the object is ALWAYS speeding up.