Re: why cannot C form C2(tetrabond)

But it can! There are many examples of dicarbon compounds - some found in 
interstellar gases, some in the lattice of semi-conductors, some bound as 
ligands within metal clusters or as the "carbide component of calcium 
carbide, and some found in the flames of a fire.

However, I think that what you are really asking is why isn't dicarbon a 
common molecule like, say, dioxygen or dinitrogen? The answer is that the 
compound is reactive, having a low lying excited state which generates a 
radical. Simple MO Theory would predict that dicarbon should have a 
double bond with both components having pi character. That is, each 
component of the bond is low energy. Lying just above these is an orbital 
with sigma character arising from the sigma overlap of the p-orbitals. 
Because it is easily accessible energetically and the radical species 
formed would react rapidly, it is not a particularly stable species 
(stability is a consequence of kinetics and thermodynamics). In the 
absense of other compounds, though, such as in the vacuum of outer space, 
dicarbon can be quite persistent.

More common is the dianion - which is the actual species in calcium 
carbide and that found bound in metal complexes. In this case, exitation 
is difficult and the species does not have an "easy" kinetic route to 
decomposition.

Hope that answers your question.