Why carbon doesn't share all it's four electrons with one carbon?

To do that  it would need to pack all the electrons into the space between the two atoms but electrons repel one-another.

On the other hand, in the vapour phase at least some of the carbon atoms go round in pairs. It's not clear that they have a "quadruple bond" between them.

With bigger atoms (where the electrons are not so tightly packed) you can get quadruple bonds.

https://en.wikipedia.org/wiki/Quadruple_bond

 

3 hours ago, John Cuthber said:

On the other hand, in the vapour phase at least some of the carbon atoms go round in pairs. It's not clear that they have a "quadruple bond" between them.

I presume this is a dynamic equilibrium situation. If so, do we know what the average 'lifetime' of a pair is?

It's hard to say.

There's some information here

https://en.wikipedia.org/wiki/Diatomic_carbon

 

But, as far as I can see, there's no reason why a single molecule of the stuff floating in space shouldn't last practically forever.