Apparently [diatomic carbon does exist](https://en.wikipedia.org/wiki/Diatomic_carbon), but it isn’t energetically stable at atmospheric pressure and temperature.
It looks like C2 creates some unique molecular orbitals that likely create the energetic instability. In addition, it looks like C2 ends up lending itself to polymerization, i.e. more carbons bonding to the ends. Unfortunately, I can’t provide much of an answer beyond that.
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