Why not mix meat or poultry with fish?

You're wrong in your observation to begin with. There are tons of things with meat and seafood:

• Cajun food often combines sausage, chicken and seafood (e.g. gumbo and jambalaya)
• "Surf and turf" is a catchall term for red meat plus seafood in American-ish cuisine, and comes in all kinds of forms (each separately, one stuffed with the other, a burger with both, both over pasta, etc)
• Asian food often combines shrimp and pork (e.g. dumplings and spring rolls)
• Paella often has sausage and seafood

(thanks to Catija for most of the examples)

That said it might be somewhat less common for a few reasons:

• Seafood tends to cook very quickly, while meat and poultry take a bit longer, so sometimes it's easier to not mix them.
• Related, seafood is often much softer, so it doesn't match textures as well as various meats and poultry. (This is especially true of fish.)
• In many areas seafood is more expensive so when people do use it they'll try to make it the star of the show, rather than combine it with other things.

And of course, simpler dishes tend to be more common, so you'll see much more with one kind of meat. Sure, there are more seafood-only dishes than combinations, but there are also more poultry-only and meat-only dishes than combinations