I grew up thinking that this was correct. "Just got my teeth dirty, time to clean them."

At some point, I heard that the opposite was true, ostensibly from a dentist on reddit. According to this anonymous stranger, after eating, your enamel is at its weakest, and you'll do the most damage to your teeth by brushing them. The reason was something about saliva and/or plaque that's been recently fed, I think.

(As a side note, some other dentist(?) in the same thread said that if you're going to brush your teeth once a day, it's most important to brush before going to bed.)

My wife hates her unfresh breath so much that she won't eat before brushing.

I don't really get it since my mouth tastes like mint for 30 minutes after brushing, which makes food taste gross.

Does she not brush at night before bed?

That's the best time to brush. Otherwise, all the bacteria and the like in your mouth have all night to fester.

Most (?) of people brush before bed and after they wake up (before breakfast).

I also brush after breakfast, but this is kinda of common knowledge so I'm surprised you don't seem to know it.

My morning routine has always been to get up and use the bathroom, brush my teeth and then go about the rest of my day. If I eat breakfast at all, it's likely to be either after I've already left the house or the last thing I do before I leave. I've read somewhere (not sure how true it actually is) that you're not supposed to brush for half an hour after eating, so there's basically no point in time where I could brush after eating breakfast.