The words 'set' and 'off' have many meanings. When they are combined, they create a new meaning. Learning these meanings is a challenge. It is very good that you have looked up the definitions of 'set' and 'off'. 'Off' also means away from, or a direction away from. Setting off on a journey means that someone moves in a direction away from where they started.

Sonenko, I'm sorry to tell you this, but you are wasting time, energy and brainpower trying to break down phrasal verbs into their constituent parts. Your teacher should have told you this with the very first phrasal verb which he or she taught you. There no connection between the word 'set', the word 'off', and any of the meanings of 'set off'. Nor is there often any connection between the various meanings that can be represented by the same combination of words. 'Set off' can have several different and totally unconnected meanings. So can most phrasal verbs - take 'make up', for example. Please do not waste any more time trying to approach phrasal verbs in this way. It will get you nowhere. You need to approach them from the way that native speakers do - by how we use them and in what contexts.