Hi! Welcome to Eorzea!

Leatherworkers (and all DoH/DoL) have 2 "weapons" - main hand and second...maybe you are trying to equip the secondary tool whilst with your PUG mits on? Thar definately wont work!

Assume you have joined the Leatherworker guild and what not?

When you equip a new weapon/tool, and dress yourself appropriately you can create a character set, for easy switching. Go to your character window, and above your picture there is an icon (like a paper list). Click on this. It opens all your registered sets. At the top of this pop-window is a little button with a + sign. click on that to register the new set. It will then be available for quick change.
Remember to update your sets whenever you buy/gain/win new gear (little ciclical arrow button near your gear set list icon in the character window).

It sounds like you are trying to equip a secondary tool, tho - so just make sure you use the Leatherwork Primary Tool....and then register your set (as above), so changing will be lots easier