It can be confusing. Some countries have explicit rules (US for example) about using that country's passport for exit/entry. It's worth going to the web site of every country you have citizenship to see if they have published guidelines. Airlines seem to mostly care about whether you will be refused entry at your destination, so if the passport you give them does not have a visa for the destination (or cannot enter the destination country without a visa) then they will start asking for additional documents.

And then there are other countries which are making a token effort to curb illegal immigration and if you present that country's passport on arrival and don't have a visa for the country you came from they will start asking for additional passports. *Headache* I just carry both all the time.