"Are you a vegetarian?"
Wow so eating vegetables makes you a vegetarian? I didn't realize I had to eat meat with every meal to keep my club membership!
Anecdote time: I looove me some meat, but I have vegetarian sausage patties in my freezer. I bought them because I wanted sausage in patty form and all the real pork was links - not helpful if you are trying to make a breakfast sandwich. I found the veggie patties to taste good enough, but were too dry to stand on their own. No matter - I plan to crumble them up and use them to make a less fatty 'sausage' gravy. Regular sausage is still awesome, but meat substitutes have come a long way and I'm not adverse to experimenting with other forms of protein as long as they taste good. Speaking of tasting good...
So by your coworker's logic, anything you aren't eating right that moment has been stricken from your diet? Or maybe it was specifically because it was falafel. I had to look up falafel, and maybe they weren't 100% off base - there is not a meat version of falafel, it is considered a substitute for meat. Is it completely off base to think that if someone is eating a meat substitute, they don't eat meat? I wouldn't assume someone was a vegetarian if they were eating a salad, but since meat substitutes are considered just that I would probably wonder if someone was eating one because meat wasn't an option - that's the primary reason they exist. You were the unfortunate victim of a food assumption, but I think they are inevitable to some degree. Lettuce and carrots don't automatically mean a diet, dessert doesn't mean you're a sinful glutton, passing on alcohol doesn't mean you are in AA, and refusing sugar doesn't make you diabetic. We eat what we eat for millions of reasons.