Dear Wandering monk,
Within two months of his joining, a fresher is allegedly shown the exit door by the Management means two things - one is that his performance is not satisfactory and alternatively the other one is that his behaviour might be very bad.
Legally speaking, the employer can terminate a fresher within the period of probation on the ground of unsatisfactory performance as per the terms of the contract of employment by means of discharge simpliciter. But it should have been well-documented for the employee has got every right to agitate it before the appropriate forum later and the forum is empowered to look into the orders of discharge simpliciter and verify whether it is colorable excercise of power or an act of victimization.
The fact that the HR asks the fresher to resign forthwith on his own or he would be terminated with bad remarks implies that there must be something fishy. Whether it is any Indian M.N.C or I.T Company, hiring freshers is not for the purpose of firing them soon without any valid reason. There must be some untold reason for such an extreme decision to dispense with the services of the particular fresher at any cost. Only the fresher alone can divulge it!