Well, it depends what period you're talking about. By the 18th century, physicians were respectable bourgeouis men. Some had higher status than others. By that point, all had to receive extensive education and training, and received the respectable title of doctor. They were drawn from the ranks of the wealthy middle class and landed gentry, because they were the only people who could afford the education necessary. So the things they did were prestigious, and they were prestigious because they did the things that they did that required learning and training.

HOWEVER, physicians must be distinguished from surgeons of the time. Being a surgeon was a distinctly lower profession in status than being a physician. Being a surgeon in those days of no anesthesia, dull instruments, and dirty and disgusting procedures, was a disgusting job. Surgeons were not gentlemen. They did not have the title of "doctor." They were called "mister". This marked them as not having the advanced, formal, expensive education that the higher class physicians had. Surgeons apprenticed to other surgeons, rather than going to an expensive school. Many surgeons were in the military and performed extraordinary procedures, ones that a person might be expected to need only once, or never, in their lifetimes. This is not something that a higher class person, with more options, would choose. A physician would get to know people and visit them with some frequency to deal with ailments. They became respected members of the community, while surgeons did more of the grunt work. Nowadays, surgeons are the MOST prestigious of people in the medical profession, but in the UK, in recognition of this history, they're still called "Mr." rather than "Dr." Many professions had this division into higher prestige, more formal education duties performed by higher classes, and lower class positions performed by less educated lower class people. Like among lawyers, there were solicitors and there were barristers. Solicitors did the grunt work (they solicited clients, spoke to criminals, visited jails, which were tasks too grubby and tradesmanlike for the landed gentry) while barristers went to court, made arguments, dealt with the finer points of the law, drafted important legal documents, that sort of thing.

So basically, these professions became higher in status as they began to require more training, so wealthier, higher status people were the only ones who could undergo the lengthy training to do so. The professions became associated with higher status people.

Here's my opinion about what happened with teachers. Back when women were limited in the careers it was appropriate for them to engage in, many higher prestige women were teachers--one of the few professions it was polite for them to do. You'd see some of the smartest, best educated women become teachers. But as more jobs opened up to women, some of the best of the best still gravitated towards teaching, while others did other things. Simultaneously, we saw conditions for teachers deteriorate, making it even less appealing for people who had other options. Of course some of the best, most dedicated people still became teachers. But with so many other options, the pool was diluted.Simultaneously, there were a lot of social problems that arose in the US, and teaching conditions became more difficult, and the situation just diminished from there. You also see things like in California, where taxes were reduced, which slashed school funding, so California went from being a place with some of best public school systems in the country, to inferior systems.