For a while I thought my halfling rogue could only DW daggers, when it seemed like a certain foppish high elf could, I attributed it to a size thing.

Turns out the short sword / long sword icons are similar enough that I should have paid closer attention to what I was doing.

I found the foolproof method - don't drag and drop gear into slots! Left click the gear slot in the equipment menu. For weapons, start with the top button for your main hand. Then left click the lower one, you'll see a list of what you can equip that accounts for what's in your other hand. I.E. a blade you can DW with in your offhand or a shield that may change the versatile options of whatever's in your main hand.