I am only starting woodworking and in several books I read that woodworking is all about prevent final product from damage of season temperature and humidity changes. So it means that to glue the bottom of the box is “the biggest evil in the world”. In the same time some famous woodworkers, like Paul Sellers, glue up the bottom of the box. I something misunderstanding or why in some cases bottom of the box can be glue up?
This is one of those things where it's partly a matter of usage — the scale of the piece, the weight it needs to hold, how rough-and-tumble the expected end use will be — but the most important issue is probably whether the bottom is solid wood or a manmade board of some kind. So the specifics matter.
As you know, all solid-wood elements expand and contract naturally with changes in humidity, and a bottom in solid wood can expand in width during the wettest part of the year which will try to force the box apart. In the worst-case scenario it could succeed by the way, especially if the box uses unreinforced mitre joints which are the weakest joint in woodworking1.
But expansion and contraction is related to the cut of the board (flat-sawn versus rift-sawn or quarter-sawn), the species used and a couple of other factors. Plus, as it's a fixed percentage the width of the piece matters. So, just like with smaller tabletops, you can often get away with ignoring wood movement if the piece is small enough.
With bottoms made of ply, MDF or HDF though, they are dimensionally stable enough that no movement needs to be allowed for at almost any scale. So in short, it's always safe to glue the bottom if it's any of those materials (or if you'd used plastic or metal, in case that's ever something you choose to do).
So, why glue the bottom of a box?
To add strength, if needed. That's it in a nutshell.
Where the bottom is not needed as a structural element, as in most small boxes made for a semi-decorative purpose2, you can easily get away with leaving the bottom to float in a groove. Obviously the box would be stronger if the bottom were glued in place, ditto if it's a mitred box having the corner joints reinforced in some way, however in real-world use neither is needed in many cases. Which is why so many boxes are built this way.
1 Especially as commonly done these days, without sizing the end-grain surfaces prior to the final glue-up.
2 I'd include many jewellery or watch boxes in this description, although obviously they are made to be used they're very much intended as beautiful decorative objects too in a lot of cases.