No, that problem was not generated by Airbnb. There’s growing demand and, because of regulation, not enough is built every year. For example, according to INE, 250k new families are formed in Spain (more than 500k people) and only 100k new houses/flats are built and the yearly deficit has been accumulating for 12 years. That is the real issue and blaming corporations is just the politicians’ easy path to deflect blame, which unfortunately too many citizens eagerly buy into.
You can exacerbate a problem (which Airbnb is doing) without being its major cause. Doing that is still bad.
Even if it were true that the problem of housing affordability was not affected by Airbnb (it's not, at best it only exacerbated an existing problem), that would not mean it didn't create other problems for cities. Having tourists concentrated in places that are not designed for it, where a hotel license would never have been issued; the problem of too many tourist accommodations, causing an overflow of tourism; problems for neighbors with parties and similar nuissances; problems with untaxed income from the smaller owners; and probably others I'm forgetting.