I would argue that in order to rationalize, you must first be rational

Rationalization is an exercise of (abuse of?) the underlying rational skill

At first I was going to respond this doesn't seem self-evident to me. Using your definitions from your other comment to modify and then flipping it, "Can someone fake logic without being able to perform logic?". I'm at least certain for specific types of logic this is true. Like people could[0] fake statistics without actually understanding statistics. "p-value should be under 0.05" and so on.

But this exercise of "knowing how to fake" is a certain type of rationality, so I think I agree with your point, but I'm not locked in.

[0] Maybe constantly is more accurate.

Being rational in many philosophical contexts is considered being consistent. Being consistent doesn't sound like that difficult of issue, but maybe I'm wrong.

That would be more aesthetically pleasing, but that's unfortunately not what the word rationalizing means.