"The number of inspiring people is much less than the number of teaching positions. And the number of inspiring mathematically talented people with enough knowledge to teach mathematics is much less than the number of math teaching positions."

I'm not convinced that that's true, in the US, anyway. There is widespread anti-intellectualism and contempt for education in this society. Funding for education except among the wealthiest schools is frequently cut. Teachers have to go on strike to get even small raises above their already small salaries, and are expected to work far beyond their miserably paid hours to create lesson plans, grade homework, participate in student extracurricular activities, and help students. At universities research and "publish or perish" are the priorities, and teaching is often seen as something to be avoided or delegated to TA's as much as possible. "Those who can't teach" is frequently bandied about. Teaching to the test, having to teach politician-decided curricula, or just babysitting students in class quite is common. Violence against both students and teachers is common.

In such a corrosive environment, is it any wonder that the most talented people might want to work in any of a number of lucrative professions, where they are highly respected and rewarded for what they do rather than go in to teaching, where they'll be held in contempt, paid a pittance, and possibly become a victim of violence?

It is my firm belief that there are a lot more talented teachers (or people who could be talented, inspiring teachers if they valued becoming such) than choose to go in to the profession, and many talented teachers who have quit the profession because they are just fed up with dealing with all of the BS and being treated like garbage. These people do exist, though, and the problem is not in having so few of them, but in the system being such that they don't want to go in to teaching or don't want to remain if they try.

"With a 100 students each semester I don’t have the time or inclination to find out about their personal struggles."

I completely understand that, and don't blame you but the system. But there is something that can be done about this. It's just that the school system and society as a whole is not doing what needs to be done: to invest much more money in to education, to make acquiring the love of learning and knowledge rather than teaching to the test a priority, to teach how to learn and not just what to learn, and yes, students' emotional needs have to be addressed. The violence we see in schools these days is but one symptom that they are being neglected.

"We are here to learn mathematics. If that is not true of a person then they shouldn’t be taking math classes."

With such a hands-off attitude, it is little wonder that so many students that don't already love mathematics or who aren't self-motivated enough to do the work are dropping out or failing.

"If a student, for whatever reason, can’t devote the required time to a course then they shouldn’t take it. The best teacher in my department, the most inspiring one too, complains about student apathy all the time. Some people just shouldn’t be in college. Many would benefit from waiting to mature and otherwise be prepared."

It would be wonderful if all students were self-motivated and love what they learn. But to leave it up to them to acquire such love and motivation will just result in many of them being left behind. Schools and societies just aren't helpless to have a positive influence on students in this regard, and we as a society would be better off if schools got more involved in fostering better attitudes towards education in their students, even if that means a greater investment of time, money, and effort.

"I can’t magically make someone want to learn."

It's not magic. It's a combination of passion for your subject and a skill of conveying that passion to others. I fully believe both can be taught. But even if they can't, there are people who have them, and there are ways to make the teaching profession more appealing to them.