The problem is The Academy's harsh voting procedure for this particular category.
The two nominated songs are shit. It's a mess.

From Wikipidea:
"While most Oscar categories have a fixed minimum and/or maximum number of nominations (such as the Best Original Score, which always has five nominations), the Best Original Song category can have a number of nominations varying from two to five. This is due to the rules set by the Academy. The rules stipulate that each member of the Music Branch of the Academy is asked to vote for their favourite songs, using a special points system using 10, 9.5, 9, 8.5, 8, 7.5, 7, 6.5 or 6 points.

Only those songs receiving an average score of 8.25 or more are eligible for nomination. If no song receives an average of 8.25 or more, there will be no nominees. If only one song achieves that score, it and the song receiving the next highest score shall be the two nominees (as has been the case in the 2011 Oscars, awarded in 2012).

Not every song used in a film is eligible for this category. According to Academy rules, a song should be "original and specifically written for a motion picture. There must be a clearly audible, intelligble, substantive rendition (not necessarily visually presented) of both lyrics and melody, used in the body of the motion picture or as the first music cue in the end credits.""

A very retarded system if you ask me, they should take the 5 highest rated as the nominees.