Why we take arbitrary current directions for same circuit
You can take arbitrary current directions but, take care. If you don't track this change everywhere in your circuit, you'll get a negative sign where there shouldn't be one, and the wrong answer (wrong circuit model).

Do an experiment, take the same circuit and draw the currents in one direction and work out the equations. Then take the same circuit and draw all the currents in the opposite directions from the first diagram and work out the equations. The thing you'll notice is that you essentially multiplied the current by -1 inverting the direction. If you take all the equations and multiply them by -1 on both sides (or any constant) you'll get the same answer.

Thus it doesn't matter which direction you take the current to be in, but it does matter that you track the direction correctly when you work out the equations.