Because they stand to lose a shit ton of money?

They lobbied and won against margarine back during WW2. It couldn't even be dyed yellow, you got a little packet of yellow dye to add to your white colored margarine at home. This lasted into the mid 1960s when they just started dying the margarine like butter.

Personally growing up on a dairy farm, I'm fine with making the distinction. Like you can't label food something that it's not. You can only call Scotch whisky Scotch only if it's made in Scotland. Same with cheeses and wines in Italy and France. It's a guarantee you are getting what you paid for, the real thing. And not some fake chemical concoction. It goes even so far as soap. Did you ever notice that Dove is called a beauty bar and not soap?

Go ahead and eat all the oat butter and drink all the oat milk you want if you like it. Oats are a pretty under used crop. The majority of it ends up as horse feed. Oats are a high food value food even for humans. I enjoy making oat bread. It's quick, simple, and tasty. Along side of a chili or soup, it makes for a hearty and nutritious meal.

Where do they sell oat butter? I need to try that

It only counts if you pour the oat milk super slow while maintaining unflinching eye contact with the staff.

Also hot is “chaud” in French which could sound like “oat”

I've seen this image years ago. I don't know how old it was already at that point.

I think this might be a meme about how the french don't like anything that goes against their national values, which heavily relies on eating "proper" food, i.e. no oak milk garbage ... but i could be wrong here.

like how they refuse to speak any language but french

Again, you vastly overestimate our level of English as a nation. The h is a super common problem. And we still think people drinking lait d'avoine are some sort of radicalised weirdos. Also TLS is a small airport, we don't do that sort of fancy stuff here.

Somebody with a milk allergy, or intolerance turned me on to oat milk.

For me, I like it better and it lasts longer in the fridge.

I haven't really tried cooking with it yet though.

I've lived in France for more than 6 years at ind point, and I can tell you that sometimes they'll just refuse to acknowledge English words.

You vastly overestimate the level of English of my compatriots. This is a 100% plausible mistake for the average English speaking French person.
Also unless it was a Starbucks or some really fancy coffee shop, we absolutely do not have oat milk as standard. And I've been to TLS, I don't recall that kind of coffee shop there.

In english, probably not. I had to look it up to know it's lait d'avoine

Ost milk

I mean, you're not helping your case here...

I think this can only come from language barrier, oat milk in french is "lait d'avoine" which doesn't sound similar at all.

Oat milk isn't rare outside the US. It's a bit harder to get in French coffee shops, but not that much.

This is just France being French. Especially because Toulouse is a small regional airport.

Personally, I agree with you. Oat milk just meshes remarkably well with the general flavor profile in coffee. It's thick, has the right general umame taste, and the texture is a lot less offensive than almond milk.

If I'm making a sweeter coffee, then I'll go for coconut. But oat is definitely superior in regards to complementary tastes. Dairy is versatile (and, IMHO, the only right way to make a properly foamy capuccino), but there's just something in oat milk that just makes coffee feel like a sturdy, rustic, wholesome drink instead of a delicacy.