Insurance is meant to protect your assets. When you are young, your biggest asset is your ‘ability to earn an income’.
So you need to consider –
Health insurance – to cover medical expenses in case you have an accident or get diagnosed with something. You may well be covered by your family’s health cover but it’s worth checking in case you’re not.
Disability insurance – to cover your liabilities or other living expenses while you are sick. Since you are young, you may not have liabilities, and your living expenses should be covered by your family. So this cover shouldn’t apply to you…and either way, it’s only available when you are earning.
Life insurance – to provide a lump sum to your dependents to replace your income, or to cover your liabilities. You need to consider that your parents may be dependents already or were expecting to become so in the near future.
So the answer depends on how ‘young’ we are talking about.