Two tailed F test, correct rejection of the null hypothesis

I am performing an F test for equality of two variances by following this website formula https://itl.nist.gov/div898/handbook/eda/section3/eda359.htm, however it states that

In the above formulas for the critical regions, the Handbook follows the convention that Fα is the upper critical value from the F distribution and F1-α is the lower critical value from the F distribution. Note that this is the opposite of the designation used by some texts and software programs.

What are currently considered the right upper and lower critical values? In two textbooks I actually found the designation opposite to the one given by the website. However,

given two samples m,n of 5 and 4 respectively,
a = 0.05,
the critical values are:
F1-a/2(m-1,n-1) = F0.975(4,3) = 0.10
Fa/2(m-1,n-1) = F0.025(4,3) = 9.97


To my understanding, F0.025 is the left tail limit and F0.975 the right tail limit. If this is correct, why has the left tail limit a higher critical value than the other?