Why Pvt. General Insurance Company shy with third party insurance?

I have two cars, one new Honda City (I have bought last year is insured with TATA-AIG) and Hyundai Santro , bought in year 2000. In next month May, the insurance for my Santro is going to due, so on last Saturday, I went to ICICI Bank, which is next to my society, with all the documents. And asked them to renew it for third party only. The guy who is the in charge for insurance, bluntly said to me that they won’t do third party only insurance cover. So I went into the Managers cabin and he also showed his inability and told me that they work on the guidelines issued by the insurance company. Now my question is - Why Pvt. General Insurance Company shy with third party
insurance?

It is because pvt. insurance company are here for profit only business. If you claim more than once, they just cancel the policy and send it back to you. I have a very bad experience with TATA-AIG. Now PSU insurer are also raised the standard and providing services at par with pvt. insurance company.

I would suggest – write to IRDA with the incident and IRDA will definitely take some action. This issue is very old one and IRDA is working on it.

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I went to ICICI Bank

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Better try with ICICI Lombard directly Or ask the customer care about this.