His argument is as simple as it is elegant. Put in terms of comparing a new treatment to standard, anyone who insists on a one-tailed test is saying the new treatment can't do worse than the standard. If its effect not the same, it can only be better. Tails refers to the tails of the normal and t reference distributions. Side refers to side of 0.
Some statisticians argue the word tails is ambiguous.
In that case, the hypothesis will be rejected for large values of the test statistic only.