If it's saying "You cannot synthesize with those materials," then you either have the wrong materials, or you're not on the correct job that can craft it. Double-check and make sure that you have your Armorer hammer equipped, and that you entered in the correct materials (it shouldn't matter what order you put them in).
If it says "You decide to wait until you are more skilled to attempt this synthesis," then it means you're not high enough level to do it yet, but seeing how Copper Barbuts require only a Lv5 Armorer
according to Yellow Gremlin, I highly doubt this is the case, since usually you can attempt a synthesis that's up to 10 levels higher than your current level, meaning you should technically be able to do it even if you were level 1.
But yeah, just make sure you're using the correct materials and that you're on Armorer when you do so. I've made the same mistake on occasion myself - I tried making Bronze Nuggets as a Goldsmith with 3 Copper Ore and 1 Tin Ore, and it gave me the "you cannot synthesize with those materials" message because only Blacksmith can make Bronze Nuggets. If that doesn't fix it, well... I dunno, lol.