Licenses and Certification Aren’t Necessary

I'm not a teacher, I don't have a degree in any educational studies either so you won't find me putting out any 'evidence' but this whole thing just made me 'fondly' remember my school days. Back then we had a wide variety of teachers and I remember about three people who I'd deem 'good teachers' while most were the alright kind and some were ... well, people who probably shouldn't teach.

So here's a bit of my experience (I should warn you that this is long but I have a hidden TL;DR at the end so just go look for that if you don't care about anybody's experience.):
- I had an English teacher that was said (nobody ever showed me their license so this is only by word of mouth) to have been working in some factory before and only did some course when they lacked teachers and managed to get into the school. It's partly thanks to this person that my English pronunciation is not up to par (trying to salvage it on my own now but it's hard if you've done it wrong for years) because they needed 3(!) years to point out there was a problem but they never offered any help on how to change that (even though we still had a year left with them). They also taught the whole class the definitely wrong pronunciation for some words which was luckily rectified two years later when we got into different courses and had a new teacher.
- I had a licensed teacher for some subject that incorporated economics, technical stuff and work-related matters. The person was a drunkard that would go and 'copy materials' only to come back without anything whatsoever and then went back to get it because he 'forgot'. Nobody wanted to get even a few steps close to them because you couldn't take the smell.
- I had a licensed teacher who managed to fail their exam twice (as he very proudly told us) but managed to get through on the third attempt. Never learned anything until a to-be teacher currently doing their internship at our school took over the course for two years. Sadly, the person was unable to salvage the situation especially since we got the old teacher back in our last year.
Btw that guy was highly unprofessional. If you were a girl and showed some cleavage you easily got full marks in his course and I had the displeasure of hearing stuff like 'A pretty girl like you should do something in the media' when casually talking about what I intended to do after school. He also had no concept of personal space and even if you shifted away from him in a conversation because you were very uncomfortable with him standing so close, he would just follow you around the room.
- In regard to the internship there's another funny story: The one who tried hard to make up for what that old teacher more or less ruined got an average grade when her course was graded later on. Another internship-person we had at the same time for our history course and who was unable to control the class (people were playing bingo, surfing on the net, talking so loud that you could hardly hear the teacher talk) and was unable to answer anybody's questions (he'd start and then drop off somewhere in the middle) got through it with the highest grade.
Oh, this guy was also the person that prompted one of my classmates to ask the director (who was our history teacher in the next year) why we weren't talking about WWI at all and he just wanted to do WWII with us. Turns out the internship-guy had managed to talk about the stuff before WWI for so long that we missed an entire semester (!) of stuff we should have known. (Which made quite a few people panic because history had an oral exam for several people at the end of school and if you miss that much it's very hard to make up for it.)
- There was also our teacher for political education. He had studied politics but didn't have a teacher's degree. He certainly knew a lot about politics. Sadly, I don't. When we were voting for the Europeen Parliament this year, I had to effing google what it was about and how I was supposed to vote for it. The only thing I actually remember is something about 'Pareto' and some principle where an exchange is supposed to be beneficial to both sides?

These were my worst experiences with teachers I guess. As for the three I'd deem 'good teachers'? Well, two of them were licensed. They taught us what they were supposed to teach us, managed to do some extra stuff, showed actual interest in their students (aka you could always come to them and ask stuff if you didn't know, even if it wasn't about the subject) and one of them even managed to inspire me personally for the following years so that I didn't give up when things didn't go well for me.
The last one wasn't licensed. He was our art teacher and I value him because we did some of the most interesting projects with him we ever did in art class. There was one problem though: He was completely unable to explain what the heck he wanted from us. He literally once told me to 'do nothing' for a project and I didn't understand. I finally did whatever I felt like because at that point, I felt I could only go wrong anyway and his final evaluation after looking at the thing was 'Oh. I actually thought this wouldn't work.' Well, I do expect of my teacher to be able to explain the effing tasks and tell me if he thinks stuff goes wrong because my fucking final mark depends on his course too. I'd deem everything else unfair. So even though his ideas were interesting - and his personality was great - these two things are why I'd say he's a 'good teacher' - he was also kind of bad because he nearly ruined my grade (and that's a huge thing because one of the universities I wanted to apply to had a minimum grade you needed to reach).

Anyway, here probably comes the TL;DR from my experience: A license doesn't guarantee that a teacher will be a good teacher. (I don't think anybody here ever said that though?) But not having a degree doesn't guarantee anything.
From my perspective as a student, I'd still rather have teachers that are certified because at the very least, I'd know they went through some basic stuff and will know what they're supposed to teach us and when. Sure, there will be slip-ups but overall my trust in them will just be higher because I know they did something to get that license.

Oh, fun fact (not my experience though): There were some cases of teachers faking licenses and teaching for several years here in Germany. The students noticed because they didn't learn anything, reported it but (at least in the one case that I remember, the woman was teaching some religion and ethics-related stuff I think) the person in question moved away so the school didn't pursue the matter. The same happened with all subsequent schools where she went until one finally managed to get onto her case and reported her.
I think it's very interesting that the students notice. It just goes to show that just because somebody thinks they can teach something, it doesn't mean they really can. Children aren't stupid. If you're not qualified (regardless of whether you have a license or not), they'll catch onto that quite fast.

Actually, it doesn't matter whether it's true or not, does it? I mean this doesn't really have anything to do with the original question - which was "Does it make sense if someone with a Doctorate in Mathematics isn't allow to teach math b\c no teaching degree/licence" (just as a reminder in case somebody can't remember after 50+ responses - I often have that problem )

I think most of us (maybe even all?) can agree on some things:
There can be bad licensed teachers, as well as bad un-licensed teachers. Likewise, there can be good licensed, as well as good un-licensed teachers.
Maybe most of us can also agree that different people will learn better in different environments and with or without other people around them. Some children will do great in a class, some children won't and will have a better experience if they're taught at home by their parents, by a private tutor.
There are many things that play into this. E.g. learning in a class doesn't just have to do with the student-teacher relationship but also with student-student relationships. I could imagine that a student that is continually bullied by their classmates will have a very hard time keeping up with their studies regardless of how excellent the teacher is (or whether they have a license or not).

I'd also like to add that people normally don't just learn from teachers. We can learn from any random dude passing by because everybody has things they will know better than others. Some of these people are great at teaching others, some people are just better at learning things from other people even if the average person would say they're very bad at explaining things. This is a matter of interest, intelligence (sorry, not trying to be mean here), time ... - you name it. Many factors play into it.
So, in a nutshell, I think that the whole situation of education is much more complicated than having/not having a license.

In regards to this discussion: I think people have given good reasons and examples for why they prefer teachers to have a license. Just off the top of my hat: That can be everything from being able to trust the person more, to making sure the person knows their stuff in regards to education, to legal reasons ...
In other words, you've actually gotten your answer already. People have told you why they think licenses do make sense in their opinion. Whether you agree with these things or not is an entirely different matter and you're the only one who can judge that. I also don't think that there is any need to 'convince' (since I think I saw this come up somewhere) anybody here. We don't need to have the same opinion on this at all.

Licenses can also be about accountability and limiting access to items.

As someone who was on the front wave of having to get certified and licensed to use certain classes of refrigerant in the U.S., it wasn't about the ability to service HVAC/cooling systems...it limited individuals from having selective deniability.

That doesn't mean it's a political tool or a form of capitalist's control.

It's so Joe Moron had to account for usage and not drop multiple cans of R-22 into a leaky system.

Not here to debunk I started off reading along and participating because you gave out some blanket statements before on new age medicine that made it sound like all of it is licensed. I am also pointing out that control isn't bad in itself because from most of your statements it comes off as you saying that it is a terrible thing.