the stairs climbed is not occurate, why?

I agree with LD150 on this. For whatever reason, Apple uses 16 steps as a "flight". I've never lived in a house that has that many stairs in one flight so, I almost never see an accurate reflection of how many times I've gone up the stairs in my house (14 steps). It does a pretty good job of capturing the fact that I climb 53 steps up from the subway. However, the actual number of flights it shows that to be varies.

It never has counted anywhere near enough flights nor has the iphone on its own.

You could contact Apple Support directly. Depending on your region, you may be able to reach them here 

Click here >  Contact - Official Apple Support  

or phone numbers 

Click here > Contact Apple for support and service - Apple Support 

I have 13 and the number of trips to the bathroom are drastically underestimated for a man of my age.

As a woman of a certain age living in a house with only one bathroom which is on the second floor, I can empathize.