A couple of things:
(1) AARP sends out many physical mailings -- asking for donations, offering insurance plans, etc. -- so the volume of waste paper that the recipients need to throw away (or "recycle") is large. Many national organizations do the same: I have heard that the NRA ("National Rifle Association") does this as well; and of course any alumni get voluminous mailings from the universities from which they graduated. The volume of the mail is not a distinguishing characteristic of the AARP, because so many other groups follow the same practice; but it is a characteristic. If it irks a lot of people, that's because they mail to a lot of people.
(2) AARP lobbies (attempts to persuade) Congress for financial advantage for older people. Some of the results may be beneficial to the nation, but some of them may be obstacles to fairness.