"You are looking sad" and "You look sad"

I say this, it is 100% grammatically correct. Just because something isn't a commonly used phrase, that doesn't mean it's wrong. As a language learner, keep in mind that sometimes people will judge what you say based on "common usage" whereas native speakers can make up new ways of using the language and don't get judged the same way. Your teacher is wrong. It may not be the most common usage, but it is certainly not incorrect.

I disagree with your teacher. What's good for the goose... Have to say, though, I'm a fan of economy and tend not to use the progressive tenses unless I really need to.

English speakers aren't very good at keeping track of- or using- our own rules. Especially American English speakers. In this case you would use "you look x" for both, though; "you look tired" or "you look sad." I wouldn't say "you're looking sad" or "you're looking tired" without sticking an adjective in there ("you're looking very tired" or "you're looking a little sad"). You might hear someone say "you're looking good" to compliment someone, especially if they haven't seen them in a while and/or if they've been sick or injured, but that's about the only example I can think of where that would be the case.

Americans will say - “you look sad” - “you look tired” “You are looking X” isn’t wrong, but it’s not how we normally say it. In fact, the only time I say “you are looking…” is if I’m being facetious: - “you’re looking chipper” to someone I’m friendly with who seems grouchy - “you are looking radiant” to someone I’m friendly with who seems hung over.

I disagree with your teacher. I would never say you are looking tired. I would say both you look sad and you look tired.

Damn. I am not sure why but she is right but with a caveat. If you put an adjective in the phrase "You are looking sad." such as "You are looking pretty sad." or "You are looking a little sad." That sounds correct to me in American English. Though I would use a contraction 100% of the time. "You're looking a little sad." I would never say "You are looking sad." You are looking sad is grammatically correct but I would never say it like that. I would say "You look sad." though. English, especially American, can have a lot of grammatically correct phrases no one would ever say and I think this is one of them.

I don't know all the technical rules. In normal conversations, I would say "You look sad," and "You look tired."

I (native speaker, US) would say all four. It just depends on the feel of the situation. “You are looking…”, or more likely, “you’re looking…”, makes it more immediate, more intimate. “You look…” feels a little more detached. The idea that any rule excludes any of these forms is ludicrous.

Best way I can explain it is that, at least for American English, the present progressive verb tense is normally relegated to describe currently enacted physical actions. “I am running”. “I am going to the store”. “I am sleeping in a bed”. If something currently expresses a passive state, the present indicative is used. “He smells funny.” “He looks tired”. “You have a big nose”. And, while the present indicative is normal for the latter category, the present progressive is generally acceptable. I am not sure why your teacher said “you are looking sad” is the better way to write that sentence, though.

"looking [adjective]" is not an action, it's a state. Present continuous is used for actions that are being done at a precise moment. You cannot be caught in the act of looking sad, nor can you be caught in the act of looking tired. Note that this is a general rule, but there are exceptions. https://www.scribbr.com/verbs/stative-verbs/#:~:text=Due%20to%20this%2C%20stative%20verbs,m%20not%20feeling%20good%E2%80%9D).

I wouldn't say "you are looking tired" either

Both of these are fine, but "you look sad" is more common

I'm really not sure what distinction your teacher is trying to make. Sad and tired are both adjectives. Someone can be looking tired, or be looking sad. I agree with what most people have said, I would use the more simple praising more commonly. "You're looking kinda tired" is very normal though. Same for sad, I just wouldn't really say someone looks sad, more because it's a bit too intimate for me. But grammatically it's fine.

It is correct, however, people (at least in the US) tend to say “you look sad”

I think it might be either personal style or regional. I would, and do say both "you look sad" and "you are looking sad". There's a nuance in meaning that I tap into when I choose which to say. Your teacher might be correct that there is a rule that someone somewhere wrote down. Day-to-day, nobody cares about these kind of obscure rules.

They are both right, but "you are looking sad" just sounds blocky, and no native speaker would say that over "you look sad"

You are looking sad seems to suggest an observation tied to the present moment only whereas you look sad doesn't necessarily need to be and could apply in general. Also you look sad seems almost like a conversation opener, and feels emotionally weighted. You are looking sad feels almost like a surface level comment, potentially even showing low concern through veiled emotions. They are both correct though. You look lost and you are looking lost. You sound tired and you are sounding tired. 退屈そうだね and 退屈そうに見えるね

"You are looking sad" is not incorrect. We typically say you look sad, but you're looking sad is acceptable.

Both are correct, the first one is just informal.

It's not incorrect, it's just rather unnatural. "You look sad" is such a common phrase; we wouldn't normally say it in a different way.

They’re both fine. There is more of a nuance of “right now” with “are looking”, in the same way as “he’s wearing red” suggests today and “he wears red” suggests often or always. Your teacher may be working off the rule that we don’t use stative verbs in the continuous tense. We would say “He has blue eyes” but not “He is having blue eyes”. In reality, though, there are lots of exceptions to this “rule”. McDonald’s slogan “I’m lovin’ it” is probably the best known example, but take also “he’s having a fun vacation”, “she’s feeling under the weather”, “I’m thinking about my lost love”. The key difference is that these all refer to temporary situations. I might think about my lost love for a while, but it would be a real shame if this was my basic state of being.

So for both you say "look" not "looking". Looking is not incorrect it is just less commonly used. It's such a small difference but basically "look x" describes the person "looking X" describes the actions of the person. So if you look sad, the person is displaying a sad emotion or appearance. If you are looking sad, you are performing actions in a sad way. Which is such a subtle small change that usually both are happening or accurate because if you are sad you probably are displaying sadness in your face and walking or talking or acting sad right. But because look is shorter usually the average person would say "you look sad" With you're looking tired, again not wrong I guess for her maybe where she's from it's more common to hear that

I think “you’re looking sad” is perfectly acceptable, but “you are looking sad” sounds awkward.