Why do I as a seller need to show my bank statements to the buyers mortage company?

It's not that the law requires this--it's that the bank is insisting on it. And the law allows banks to set their own requirements for extending loans, so long as those requirements do not discriminate against a specifically protected class (e.g. no racial discrimination in lending for housing). For some reason, this bank wants to see your statements--you are free to ask them for "why." If they will not tell you, you don't like the answer, or generally either don't trust them or don't want to do this, you can refuse--though in that case, the loan may well fall through, and the buyer may have grounds to get out of the contract of sale, especially if there is finance contingency.

(As for "why"--perhaps the bank fears that you do not have the financial resources to meet your own closing day obligations and is worried that the deal may fall through at the last  moment; or possibly the bank is worried that there is something untoward going on--for example, that you are actually loaning money to the buyer to let them "buy" your house at  higher price than it appraisers for, for some reason.)