It’s good that you are covered under a group health insurance policy provided by your employer. But generally, insurance covers provided by employers are of a lesser sum insured, which seems to be insufficient in case of any medical emergency. Most group insurance policies have co-payment and high deductibles in-build, due to which you may require to pay from your own pocket.
Another reason, why you should have a separate policy is, you cannot be working with the same company for whole life, and as soon as you leave the job, your previous employer may take back health benefits, and you might not get such benefits from your current employer. As a result of this, you’ll have to buy a fresh policy in which you’ll lose pre-existing benefits that you have accrued over the period.
By buying a separate health policy, you can choose cover amount and other benefits as per your medical requirement.