Probation Notice Period - Why company giving 30 days of notice, what if I need to resign? Why should I serve 2months?

I joined my current company 3 months back, I am in my probation period. I want to resign.
In offer letter they mentioned like this,

1.2 The Company may at its sole discretion extend the period of probation for such further period as it deems fit, or it may terminate the employee before the completion of the period with or without cause upon written notice of thirty (30) days or pay in lieu thereof.

In termination: subject to clause 1.2 either party can terminate - notice period of 2 months.

Why company giving 30 days of notice, what if I need to resign? Why should I serve 2months?
would they allow me to serve 30days?

The poster should have raised this question before accepting the offer or before joining the service.

If we analyse the paragraph 1.2 and the termination clause in juxta position, we have to understand and accept that both are different in their operations.
Paragraph 1.2 is specific about the notice condition to be complied with by the employer if he terminates the service of the probationer in stead of extending his probation period whereas the termination mentioned subsequent pertains to the notice condition of unilateral termination of the contract anytime after probation. In other words, the employee has no choice of terminating the contract of employment on his own during the period of probation and in case he desires to do so, he has to comply with two months notice clause applicable to termination in general.

Why this inequality can be a pertinent question. But it should have been raised before accepting the offer or joining the services like I mentioned at the outset. The employer can argue that the purpose of appointment is not firing afterwards and the period of probation is only a phase of orientation to make the new recruit adaptive to the work culture of the organization and it is the responsibility of the probationer to complete it successfully at least with extension and termination at this stage is only an inevitable alternative to the employer when his performance is beyond any redemption.

Any way, my personal view is that it should also be of equal duration to both the employer and the employee in respect of unilateral exit even during probation.

Your question is valid and for you the notice period is 30 days. The employer is wrong to ask for 60 days notice because as per the terms of your appointment. You better need to send a notice from a lawyer to have settle the matter in legal way.