Song Mixing can be defined as;
1. Making the band sound like they want.
2. Making the establishment owner happy (make the pastor happy).
3. Making the music sound "great."
4. Making a speaker's voice easy to understand.
5. Making cheap instruments sound like expensive ones.
These can all be valid points but each one misses the mark. Each one of these defines a fraction of the mixing realm. In other words, each one is a small slice of the mixing pie.
Song mixing is creating a sound that invokes an intended emotional response from the listeners.
The band wants the audience to feel the emotions their songs are trying to convey. The pastor wants the music to have a worshipful feel. The audience (the congregation) wants to feel moved by the music. It's up to you to do that. Making a small guitar sound big or a piece of junk drum set sound like a set of expensive ones is just part of the process that takes you toward achieving that emotional state.
Mixing is not pure science.
Mixing isn't about setting EQ's the same way all the time. Mixing isn't about setting the volume levels once. Mixing isn't about one-size fits all. The scientifically-minded people can easily lean this direction. IF acoustic guitar THEN cut high-end EQ at 8 KHz. Sorry, but it just isn't that easy.
Mixing is not pure art.
It's true that a person with an ear for mixing can do a good job with little knowledge of the science. However, they could still be better if they understood the science behind it all. That leads to my next important point.
Mixing is a combination of art and science.
A heart surgeon has one goal in mind; heal the patient. This requires the proper staff, the proper (and sterile) tools, and the proper knowledge so they can do the tasks which lead to reaching their goal. That's exactly how you should thing of mixing. The goal is creating a sound that invokes an intended emotional response. But it's getting the details right that enable you to do that. Keeping the goal in mind, you'll do what you need to reach it.