I recently bought a white skirt tetra, and he seems to be a little on the aggressive side toward one of my Cory Catfish. This Cory happens to bee the crazy one that likes to swim really fast all over the place. When the Cory get's close to the Tetra, the Tetra starts to follow it and bump into it. He keeps doing this, and sometimes he tries to just find the Cory and bully him like this. Is he being aggressive or is he just playing? or is it his way of telling the cory to "Calm down"? I don't know if I should take out the Tetra or not, but I don't want any of my fish dying either.
The answer from Karl is surely a good one. But I think there might be another reason too. White skirt tetra are a school fish. The recommendation is to keep minimum 5 together. If you really bought "a tetra" you simply need more. I don't want to recommend buying more directly since we are missing information on your tank overall. 5 fish and a 20 gallon tank is the minimum you need to keep this fish healthy and happy.
Corydoras need good hiding places (Sterba 1990). The fact that the Cory is swimming fast might indicate that they're missing/not sufficient. Increasing hiding places by adding fast growing plants might solve the issue.
If not, this behaviour justifies to separate Tetra and Corydoras into different aquariums. I'd move the Tetra out.
STERBA, Günther. Süsswasserfische der Welt. 2., durchges. Aufl. ed. Stuttgart: Stuttgart : Ulmer, 1990.