Legally, no seller has to pay for a home inspection but if your house has been on the market for some time and the buyer now wants you—the seller to pay for a home inspection—and you don’t—it could be a deal breaker.
Further, whoever hires the home inspector holds the largest interest in the results. If you, as the seller, pick a home inspector and pay for it, the inspector’s loyalty will fall to you as you entered into a contract and paid for the service.
If the buyer hires a home inspector and still wants you to pay for it—even if the inspector was hired by the buyer—since you, as the seller, are paying for it—the inspector will or at least should, consider you as their client.
So, as a seller, you don’t have to comply with finding or paying an inspector—but again, it may be something to consider to aid in closing the deal.