Solved – Advantages of using independent samples T-test over one-way ANOVA for comparing two groups

With questions like this there is always a bit of ambiguity, since there are lots of different tests that use the T-distribution as the null distribution, and hence, are referred to as "T-tests". Comparing to the ANOVA test requires consideration of which particular T-test you are talking about.

Gossett's T-test (the two-sample t-test with assumed equal variances) is formally equivalent to a one-way two-group ANOVA test from Gaussian linear regression. For these tests it can be shown that $T^2 = F$ and so the p-values of both tests are the same. Since these are the same test, it makes no difference which you use. Where the T-test becomes "more flexible" is when you remove the assumption of equal variances for the groups and use Welch's T-test or some similar variant. With this variation you now have a T-test that is not equivalent to the one-way two-group ANOVA test from Gaussian linear regression. The greater "flexibility" occurs because the test accomodates cases where the variances of the two groups are substantially different.