Reason behind the choice of the 0.05 p-value threshold value I just would like to understand the basis and rational why 0.05 is widely used as the accepted value to decide rare or unlikely.
Is p-value threshold related with the confidence interval or +/- $2\sigma$ as the basis for 5%?

I think that is the opposite.  People first started to use 5% as the threshold for "rare" events.  Then, since the 97.5-th percentile of the standard normal distribution is around 1.97, people also started to use the 2$\sigma$ rule for convenience.
In my understanding, choosing 5% in the first place is only a historical convention.
I would be interested in hearing other opinions, though.
