Because the law hasn't caught up to reality yet.
Airbnb has made a significant positive difference in my own life. I would've been in a bad spot if not for the places I found via Airbnb. No idea whether the transactions were legal, but in the end I found a place to live and the host found a tenant. Win-win.
The problem is when people rent these places and then throw loud parties. The neighbors' rights are violated in that case. I don't know of a good solution, but I don't think it's worth sacrificing the entire platform due to that problem.
EDIT: It seems like if people here were given the option of either casting me out into the street or letting me rent an Airbnb apartment, some would honestly and truly choose the former.
In the part of America I was in, you can't get an apartment without proof of employment, unless you have more than $15k in the bank. (Something like a year or two worth of rent. I forget the exact amount.) I was between jobs at the time, and needed a place to stay to get another job. So, which illegal act would you have me do: Get a friend to say they were "employing" me as a consultant, or rent an apartment via Airbnb? Why would you be okay with the former, but not the latter? And if you're okay with neither, then what would you have me do?