Depends on︀ the country, many countries accept that you enter and leave on different passports, but some︁ dont. For example, if you travel between the EU and Africa and have dual EU/African︂ passports, which is very common among the African diaspora in Europe, you basically have to︃ use the EU passport to travel to the EU. The alternative would be to go︄ through the time consuming and very bureaucratic process to get a Schengen visa - that︅ doesnt make sense at all if you have an EU passport.
Likewise when travelling to︆ Africa, you are going to use your African passport, as most African countries have visa︇ requirements for EU citizens, while not as paperwork-intensive as Schengen requirement, they can be capricious︈ and random. At check in in the EU, you just show the African passport and︉ no need for extra paperwork. Likewise on arrival in Africa, it s a much smoother︊ experience travelling in on the local country's passport than on a foreign one.
EU countries︋ typically never have a problem with people leaving on their other passport (as long as︌ they were in the EU legally) - there is no side room issues. I know︍ people who have travelled like this for 30 years without any problems.
