Imagine that you have the perfect trading system. With this system you ALWAYS buy at the EXACT low and sell at the EXACT high (and vice versa for short position).
The average yearly move of the British pound (GBP/USD) is 2000 pips.
The average daily move is 100 pips.
The long term trader will make 2000 pips a year with this perfect system.
The day trader, on the other hand, will make 100 x 250 (days) = 25 000 pips that same year with that same perfect system,
more than 12 times more money.
This simple example should give you an idea of the profitability of day-trading systems (compared to long term trading), even at the intuitive level.