Why most trainers recommend you to train your abs every day? Why are they not respecting the 24-48 hour training window?
It depends on the "training", like any other muscle or muscle group.
Typically people are not approaching their 1RM or training their abs for strength, and as such they're not tearing down the tissue as much. If you were doing something like weighted inclined crunches and training for strength (maxing 3-5 reps) then you would treat your abs the same as performing any other 3RM-5RM lift as far as recovery goes: taking time off for recovery to complete.
On the flip side, if you just did the isometric support position on rings, you could do that every day because it's akin to holding a plank. They're both exercises, but similar to going for a walk there simply isn't as much tissue damage for the normal person.
Summarized, rest periods are directly related to the time it takes for your body to heal the damage you did. Most ab exercises are higher repped, and the issue is more about waste products (lactic acidosis and anaerobic glycolisis, primarily) than repairing and rebuilding torn tissue.
Edited, I found this well written answer which is possibly a duplicate question. Regardless, it's relevant.
All of your muscles vary in degree of resistibility to training. For example, you use your calves every single day, but you don't have to wait 24-48 hours to use them again. They are much more resistant to training. The same goes for your abdominals.
Another thing to think about is the way you train your abdominals. Usually, abs are trained in sets with high repetitions and no extra weights. Like running everyday, these low intensity workouts do not tax your muscles like heavy bench presses or squats do. Your body is able to recover much faster.