Maybe your phone has a duff barometric sensor. It relies on air pressure readings to figure out if it's going up or down.
When working out how many steps you've taken, it relies on an accelerometer sensor. Undoubtedly there is some internal algorithm that tries to match actual sensed acceleration with steps taken. There will always be some degree of error. For example, plopping your phone on a table and lifting it off again: is that technically a step or not.
In my experience, my phone records the number of steps I've taken remarkably well. If I walk 1,000 paces (I've tried it) it won't be off by more than a few steps. The same would not be true if I shuffled along in an abnormal walking manner.
Do some proper experiments and record the results. You could have duff sensors.
Here is some data for you: I have a 64gb 6+
1. I live in an apartment and climb 1.5 flights of stairs to get to my door.
There are times, as long as a week where Health shows no stair activity. Including store, mail, daily walks (by doctor direction), beach (I live close to it) I go up and down the stairs multiple times per day. My daily average according to my device, is 1.
2. To combat my blood pressure, I walk most evenings and mapped myself several "routes" from 2 miles to 5 miles. Health consistently under scores the distance walked. This is generally by 15 - 25 percent. I have measured the distance with my car, on Google maps and a hand held GPS trail tracker. The straighter the distance (less turns and curves) the more accurate the device is.
3. Number of steps - I took a walk on a beach path (marked in distance for joggers) walking 1.2 miles each way. Not only did the 6+ under report the distance (1.78 vs. 2.4 actual) it under counted the steps by just over 200 in comparison to a pedometer I took with me.
At this point, yes, the Health feature from an activity tracking perspective is incorrect. No, I do not think it is a faulty device. I have a peer at work who is experiencing a similar issue with his 6+.
btw: on my 5S and now my 6+, I have yet to find an app that is consistently accurate (or close) for these types of activities. As for the 6+, it consistently under reports by varying degrees. I am considering a Fitbit.