There's a disconnect between the text and the photo in the June 1 Food article "Mango's Many Sides." The text states that the way to remove the flesh from a mango is to first peel off the skin and then cut the flesh away from the pit. But the accompanying photo obviously shows a different and much better way of removing the flesh.
In the pictured method, one slices close to the pit on one side and then slices close to the pit on the other. You then have two pieces of flesh with the skin still attached. Then you make the several cross-cuts shown in the photo, stopping just short of the skin. The last step is to turn the two halves "inside out." You can then slice the flesh away from the skin to use in a recipe, or, if you want to enjoy the juicy fruit then and there, you can just scrape it away with your teeth, trying hard to keep the juice from running down your cheeks and dripping on an expensive blouse.
Finally, it's been my experience that most or all of the fibrous flesh adheres strongly to the pit during the first slicings, so there's little or none on the "inside-out" segments to worry about or avoid.
Holding a mango in your mitt
Slice both sides close to the pit.
Make many cross-cuts in
The juicy flesh down to the skin.
Now you've got the hang of it.
-- Rick Gould