Understanding Hypothesis Testing for T Tests

Question

What is wrong with the following reasoning when doing a t test for difference in means ?

(Assume this is an Independent two-sample t-test with equal sample sizes and variance)

Perform a 2 tailed test and see that there is a statistically significant difference in the 2 means.

From here, run a 1 tailed test in both directions to test whether one group has a statistically significant larger mean.

In my mind that makes sense... Test for a difference, then test for the direction of the difference.

What is the issue with performing a 2 tailed test before a 1 tailed ?

Note: I asked this before with a more concrete example, but the responses went stale