Because for some reason Tri-X just isn’t enough for me. When I want something a bit different I go for the 5222, Eastman Double-X. Reasons to use Double-X? Though grainier, it’s sharper, and it gives a different look, lovely tonality. And cost, if you’re willing to invest in a 400ft roll of the stuff!
Tri-X is an everyday film, Double-X is for special occasions, and I used it for a few specific projects including my 2-semester-long (and just wrapping up) document of making Overwhelming Majority.
This current iteration was developed by Kodak in the late 1950s and then left alone, so it will give you a classic, mid-century look, especially if you use older lenses/cameras. And that is something I recommend! It requires fairly precise exposure and development can be tricky since it’s designed to be used with Kodak D-96, and anything else will boost the contrast quite a bit. Using older, low-contrast lenses will tame that somewhat. I tend to shoot it inside if the light is good enough, or outside on overcast days. I’ve seen some pretty good results from pushing, etc, though I’ve never had much luck myself.
Here are some great resources if you’re going to shoot Double-X:
Project Double-X (sadly defunct due to the death of its owner)
Through the Viewfinder’s 400ft Roll Project
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The Resurrected Camera 
I’ve shot a few rolls of this stuff and have a few more chilling in the fridge. I like it, but like you, for special occasions.