this part of the city is going
to be too expensive for normal
people to live there, is nothing
short of theft.

I'd recommend not using terms like "theft" here, as it is factually inaccurate, and goes back to the unfortunate tradition of Leninist agitation which gave the world Stalin, Mao and Pol Pot ... and despite all the violence, didn't even manage to produce housing of a quality that came close to anything the modern western democracies had to offer to their masses. And in case of the Soviet Union didn't even manage to feed its own population.

Anyway, let me remind you that I don't believe your claim that Airbnb has a
substantial influence on property prices. As far as I can see, the
dominant factor in property prices is distance from center, and
proximity to amenities, in particular public transport -- all that regardless
of Airbnb.

because they live on the outskirts

The main purpose of public transport is to enable those living in the
outskirts to get to the center in the morning, and go back in the
evening. The drive to separate out work from living quarters goes
back to the industrial revolution when work suddenly became noisy,
dangerous and polluting, so the old model (working and living in the
same place) had to go. This required mass transport, be it cars or
public transport Anyway, there is nothing wrong with living in the
outskirts. Many prefer it, especially those with children. There is
no human right to live in Manhattan or in Mayfair or in Charlottenburg
in a 150 m^2 loft that costs only €200 per month. That would be an
extremely inefficient use of dense urban space. Second, tourists use
public transport more than the normal population, because the latter
spends most of their day working, while tourists explore and move
around. If you are interested in the utilisation of public transport,
attracting more tourism is a god-sent. Note also that increased
tourism generates additional local employment, because tourists spend
quite a bit of money.

students who can afford to take
time off and travel ARE RICH!

This is deeply misleading. In any given country, students are near the
bottom in terms of average spending power, and that's because they
typically live on their parents money and / or government grants.
Their peers who dropped out of school at 16 and learned a trade
(e.g. welding or carpentry or plumbing) will out-earn the average
student at that age (a few years after graduation this will change).
Note also that in most western countries, nowadays the majority of the
population goes to university (for some definition of university).
Another way of seeing that students are essentially at the bottom of
each society in terms of spending power is to look how they live
(eg. sharing), and to look at the population's average income
trajectory: just about anyone's overall available income increases
considerably after graduation.

Of course you can compare the average student in Denmark with the
average worker in Malawi, and find that the former is wealthy
vis-a-vis the latter, but this is not an interesting comparison.

Czech Republic is 11 000CZK

Yes, and why is this interesting? The minimum wage in Malawi is
... what $1 per year? The cost of accomodation always correlates strongly
with the average income

Poor people have trouble paying for rent

Not in a meaningful sense in the western world. For essentially
everybody by the richest, say for 98% of the population, rent/mortgage
is the single biggest cost they have in life. The average person
spends between 25% and 50% of their income (after taxes) on
accomodation. This feels painful for everybody, but is managable in
practise. Another way of looking at this is to see who is homeless, and why. In practise in Wester Europe, there is little/no
homelessness apart from those with serious drugs problems and / or
mental illness. This is a pretty strong indication that housing is affordable for everybody. Yes, it would be better if there was
no homelessness, but the problem is one of drug-addition and mental
illness, and that's something that as of 2017 we don't really know how
to solve.

And those people don't benefit
from AirBNB

They benefit in several ways: I already mentioned the economic boost
that cities get from additional tourism. But they also benefit from
the economies of scale that you get from streamlined tourism, like
cheaper flights, cheaper holidays, more interesting cities. Easier
travelling because large companies like Airbnb can develop apps that
make booking easier.