best (adj.)
1. of the highest quality or excellence, most effective
2. most enjoyable, desirable
3. most appropriate
It is an argument, of course, not a mystery. To solve an eternally rhetorical issue such as this, it is a good first step to begin with the semantics of the question. Naturally, since everyone has a personal approach to determining the "best" song of all time, we can at least agree on an arbitrary definition to come together on middle ground (albeit acres and acres of ground). So we begin with the definition of best. Best is better than the rest. It is more excellent, more effective, and more appropriate than all others. It is preferred by personal taste over all others.
The trouble is, we cannot immediately reject any song as being inappropriate or not enjoyable, because someone is sure to break rank and come to the defense of Philip Glass, bagpipes, screamo, or any other mesh of sounds deemed unlistenable by a random panel representing the majority. Even at its core definition, it seems, "best" is not universal.
There is conflict within the definition itself, too. Let's agree (to save time) that "quality" does not refer to the sound recording , but to the song composition itself. Now we are left to determine quality of a lyric, a melody, a chord progression, and a rhythmic meter. Under this parameter, the masterful melody of "Georgia On My Mind" cannot compete with the constant pulse of "Billie Jean." Conversely, the gyrating "What'd I Say" might shatter the chances of "Man in the Mirror," so we get into trouble when we weigh one musical component more than another.
Words like "enjoyable" and "desirable" are blatantly subjective. Actually, we can agree that a song gives delight or pleasure, but we disagree when we add the truly problematic word: most. The world can agree (if they take my word for it, or if they observe for themselves) that "Unchained Melody" makes my mom happy. "Old Time Rock & Roll" also makes her happy. Even though preference is a matter of personal opinion, my mother enjoying these songs is a matter of fact, and cannot be disputed (just try it with her)! What can be disputed, is the value attributed to the enjoyment of each (every) song. Who is to say that my mother receives more pleasure listening to the soothing baritones of the Righteous Brothers, or the electric growl of Bob Seger, or vice versa?
Then we have the word "appropriate," which sounds like it should be debated in congressional committees. Depending who you asked at the time it was presented to the world, "Blowin' in the Wind" was at once peaceful and inflammatory. Again, opinion rears its ugly head.
Complicating matters futher, is the quantifier "of all time." Nevermind that we cannot possibly judge every song that has ever existed (or will exist); if we cannot even settle the balance between melody and rhythm, how are we to settle a tournament of diverse participants from Vivaldi to Lennon?
So, as you knew before reading this article, the best song of all time is subject to opinion, but once you settle on your decision, be prepared to support it with proof of its excellence, effectiveness, appropriateness, and desirability. You'll have to defend your choice against a friend, who will inevitably claim your song "sucks" compared to Green Day.