Why is beryllium 8 ($ ^8_4 Be $) such an unstable element? And by unstable I mean a half life of $ 6.7 \cdot 10^{-17} s$.
And what is exactly the criterion used to say an element is stable of unstable? Where do we draw the line?
 A: One point of view is that the state of two alpha particles is not bound. A bit like the system of two protons or system of two neutrons.
The other point of view is that once you form a resonance (could be viewed as a kind of a ground state of $^{8}Be$) it immediately (in the moment of formation?) "sees" an energetically more favored state of two separate alpha particles and -since the interaction is strong - it can decay very fast to the final state (see also Fermi golden rule).
Addendum:
If the interaction $<fin|H|init>$ between the initial and final states (hypothetically) was electromagnetic, the half-life of the state could be like $10^{-12} s$ and longer (if the transition multipole is too high or the two states are too different). These are the times one frequently finds when an excited nucleus cools down by $\gamma$ emission. 
Criterion:
(I forgot)
Stability is usually ment as a stability against a decay. Look at https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html - all black are stable, they are not too many. What you mean is probably "stable or radioactive" or something in this sense. Many can decay by $\beta+$ or $\beta-$, but from the perspective of a strong interaction, they are quite stable. You can define unbound nuclei and one speaks about neutron drip line or proton drip line. Alpha decay of heavy nuclei is a bit different process to mention it here.
A: Even though the decay energy of 8 Be is far less than that of 238 U it has a short half life due to the extremely shallow Coulomb barrier. This means that the pre formed alpha particle has an extremely high probability of escaping (as you remember, the probability of the alpha particle tunneling has to do with the difference between the KE of the alpha particle and the Coulomb potential), compared to that of U. And of all compound nuclei formed of alphas, 8 Be is the only one with more mass energy than the rest. For example, 12 C has less mass energy than 8 Be, hence why it's stable.
