As Jennifer explained, the difference between “aber” und “doch (jedoch)” is VERY subtle. I think it depends on many factors such as the general context of the talk, the educational background of the participants, the social situation and so on. I would like to agree with Jennifer that “aber” is more determined than “doch/jedoch”. You could try to use “allerdings” to soften your contradiction a bit. This word is – in a business situation – my favourite one when I try to be polite but firm. Best regards, Paul

It is somewhat subtle, but "aber" is more negative, while "doch" would be "jedoch" when used as "but". I'll try to show you with an example (in English: "I'm learning, but I would rather sleep.") "Ich lerne, aber ich möchte lieber schlafen." is much more 'confrontational' than "Ich lerne, jedoch möchte ich lieber schlafen.". HOWEVER the second one is much more normal - in any casual conversation the first one is totally fine. Like I said it's a subtle difference...I hope I could help and if not feel free to ask again.