On the simplest level, ETS is just fuel rationing. Limit the amount of fuel an airline starts the year with and it has three choices - fly less, use more efficient aircraft, or buy someone else's allowance.
This particular ETS has a number of features that European airlines don't like and non-European airlines loathe. First, the total 'pot' of allowances is the 2005 level minus 3% so it's about 20% less than today's business as usual - there's no way that carriers can avoid the 'buy' option.
Secondly, 15% of the allowances must be bought anyway, from the countries in the scheme. This money just goes straight into treasuries and exchequers and the non-EU countries see this as just a cash grab to prop up wonky economies and wonky currencies.
stuckgear: there are two kinds of people in the world – those who believe that CO2 influenced climate change may be happening and those who do not. In the context of this thread it matters not at all which side you are on, because we are discussing the consequences of policy decisions already taken.
The Delhi Declaration, in which 24 countries – including China, India, Russia, USA and Japan – condemned EU ETS, contained the following words:
Recognising that international aviation’s growth makes it necessary to address the long-term growth of Greenhouse Gas (GHG) enissions that contribute to global climate change
But hey, maybe they are all wrong.