You spend your money on things just as trivial, like posting here, playing video games, or going to the theater. Should it be forbidden to you too?
Second, and that's like the third or fourth time I'm saying it, it's not politicians who spent money, it companies/private individuals. Now, since you don't seem to see why it's not trivial to their eyes, let me explain it shortly: the inauguration ceremonies are a very good place for big companies, influential people or celebrities to be seen with the new administration, to talk to them and show support so that they have influence later when decisions will affect their business area. It's lobbying, and (sadly) if you want to stand out, you have to do it. Companies did it with Clinton, they did it with Bush, and I have no doubt they will do it with the next President.
Third, that inauguration is a display to the rest of the world to show them your power/wealth.

Last, about the taxpayer money: the inauguration is in fact in two parts: there's the inauguration itself, where the President is sworn in, and one ball after. That's what is paid by taxpayers money (DC area I think), to which you add the security (which might have been a bigger part of the bill this year, since a few things happened since Jan 2001) (and some also count the "lost revenue due to the day off"). All the other side ceremonies, all the other balls are paid for by private contributors, not taxpayers money.