Why do I have to appear before lawyer regarding my stolen car

If by "the claim is on hold," you mean that your insurer is not paying until you do this, that is because unless and until ordered by a court, any payment by your insurer is essentially voluntary: that is, they agree that under the terms of your policy, they should pay, and do so. That in turn means that if they are in any way not satisified by what you put in your claim, they can request additional proof or information before they pay, including your testimony under oath. In this case, they most likely believe--or at least think there is some chance--that your car was not truly stolen, such as that you gave or sold it to someone, or paid someone to take it so you could file an insurance claim. 
You can refuse to do this. They can then refuse to pay you. You could then, if you believe they should have paid, file a lawsuit for "breach of contract" against your insurer (that is, for not paying when the insurance policy, which is a contract, says they should pay) and try to prove in court that under the terms of your policy and the facts of this situation, they must pay. Of course, in doing this, you will end up having to testify under oath, so you will have to do the same thing you are objecting to now. Therefore, you might wish to simply do the examination now, rather than later, in the context of a lawsuit.