Should you optimize tracks individually or in the context of the whole mix?
If you read the comments of pro mix engineers whenever you can (and you should) you will often find that they like to optimize individual tracks in the context of the whole mix. So, for example, you would EQ a guitar track while the whole mix is playing. You wouldn't solo the track because whatever you did to it, you wouldn't know whether it would work for the benefit of the whole mix.
But you sometimes have to take what mix engineers say a little less than literally. They might be expert at mixing, but can you also expect them to be expert in explaining what they do? Try explaining to an octo-tentacled space alien how you walk on just two legs. Explaining what you do by instinct is often difficult, sometimes impossible.
Let's suppose however that today you have a song to mix and you decide not to use the solo buttons at all. You throw up the faders and, with levels, EQ, compression and reverb, you refine and hone, hone and refine, refine and hone, until the mix is perfect.
Well done! You have created a mix where each individual track was processed in the correct context.
I would have to ask the question, "In the correct context of what?"
If you adjust everything in the context of the whole mix, then you have started with the context of an amorphous blob of audio. And then you EQed the guitar (for instance) in the context of that amorphous blob. Then you EQed something else, then something else. Basically you're going round in circles chasing a moving target. Gradually you are hoping that things will pull together and you will have a passably correct context in which to judge and adjust individual tracks. Don't worry - you'll get there in the end.
There are many ways to mix, and if the process I have described gets you to a good result, then that's fine. At the end of the day, if your mix sounds good, then it is good.
I would contend however that there is a better approach to mixing, and I suspect that the really great mix engineers do this by instinct, even if they don't realize it.
In any song, there will be certain components that are the most important. It may be the vocal, or in a more dance-orientated track it might be the combination of kick drum and bass instrument.
Whatever you choose as the most important element of your song, you should solo it and do whatever you need to to make it the most fantastic-est, exciting-est, wow-wow-wow-est it can possibly be. Make it so great that anyone hearing it for the first time will buy your record in an instant, without even hearing the rest of the instruments. OK, that's an impossible thing to happen, but it should be your aim.
When you have done that, you have your context and you can blend in the other instruments to suit the one you have selected as most important. From this point in the mix, no soloing should be necessary.
In summary, I will definitely say that there is no one correct way to mix. However it is always correct to have a plan of action. Different plans for different tracks, perhaps different plans for different days. The plan I have just outlined is a good one.