We didn't like this at all, and searched the internet for a solution, but no solution was found. So, we contacted Apple Support on twitter and they were very helpful. The matter was escalated & we exchanged troubleshooting calls and emails. They asked if I swung my arms when I walked, and I answered: "normally, but not the military walk kind of swing".
It turned out, the Apple Watch keeps track of the exercise using the arm swings. Not the distance (GPS), not my heart rate (wrist sensor), not the time, but arm swings? Arm swings also controls how much calories the watch detects you've burned.. This is silly.
So, we started swinging our arms as if we were jogging, and yippee it started registering. But how much confidence do we now have in how the Apple Watch calculates our activities? Much lower.