For large parts of London's underground (and overground[†]) it is simply the case that it wasn't really designed — lines were slapped in willy-nilly by disparate commercial interests with relatively little forward planning, and only later became something like a coherent whole with some consideration for coordinated thinking. Once the lines are in, upgrading them is more difficult than building them in the first place, particularly if you don't want to stop service for large parts of the improvement work.
> just like in any other number of countries around the world
Other cities had extra benefit of hindsight, being able to design around the problems identified in older systems (particularly London's).
> They could have used the same rails, no need for a separate line
You at least need passing places around stations in practise. In theory* you could have many extra points and pass trains between the existing two lines to work around each other instead of keeping one line dedicated for each direction (as is the case for most of the track length) even at stopping points like stations but that gets complex to manage, has more moving parts (which are difficult to maintain in the confined space), would considerably slow down flow at busy periods as the trains can't move as fast over the points (particularly if they may need to switch line at them) and will spend time waiting for an opposing train ahead to switch out of the way, the tunnel around each change point needs to be wider (for the train partly, unless you redesign them too, for maintenance even more so), … It might work for a small number of non-stop trains worming their way through the system around the majority stop-start services, but that number of services would be so small to the point where the investment would not be nearly worth the small overall gain in reduced journey times.
[†] only about 45% of the line distance of the current tube is actually underground[‡]
[‡] though that includes large overground sections in the outer zones if you are only considering central London I suspected that %age is considerably higher
> just like in any other number of countries around the world
Other cities had extra benefit of hindsight, being able to design around the problems identified in older systems (particularly London's).
> They could have used the same rails, no need for a separate line
You at least need passing places around stations in practise. In theory* you could have many extra points and pass trains between the existing two lines to work around each other instead of keeping one line dedicated for each direction (as is the case for most of the track length) even at stopping points like stations but that gets complex to manage, has more moving parts (which are difficult to maintain in the confined space), would considerably slow down flow at busy periods as the trains can't move as fast over the points (particularly if they may need to switch line at them) and will spend time waiting for an opposing train ahead to switch out of the way, the tunnel around each change point needs to be wider (for the train partly, unless you redesign them too, for maintenance even more so), … It might work for a small number of non-stop trains worming their way through the system around the majority stop-start services, but that number of services would be so small to the point where the investment would not be nearly worth the small overall gain in reduced journey times.
[†] only about 45% of the line distance of the current tube is actually underground[‡] [‡] though that includes large overground sections in the outer zones if you are only considering central London I suspected that %age is considerably higher