Teaching sports as they are taught in schools nowadays is a permissible profession, so long as the teacher strives to avoid haraam things which often occur in this field, such as mixing, uncovering of ‘awrahs, missing prayers, and going to extremes in practising sports so that they overtake other duties. Indeed, the physical education teacher has a great role to play in influencing the students’ behaviour and attitude. He is close to them because he does something with them that they love, and he can make the most of his position with them to teach them good attitudes and how to interact with others in a good manner, and he can remind them to pray regularly and on time, and do other duties, in addition to the physical and health benefits that the students may gain from this subject, if the teacher is sincere in his work and does not fall short in his duties towards Allaah and towards other people. 

Shaykh Ibn ‘Uthaymeen said in al-Liqa’ al-Shahri (14/question no. 6): 

I call on my brothers who practise these sports to adhere to Islam. I know that there are among them those who adhere to Islam completely, praise be to Allaah, but I would like them to call their fellows to adhere to the religion of Allaah, may He be glorified and exalted, and to establish prayer in congregation on time, and to wear covering clothes, and we hope that they will be guided to that which is good. End quote. 

Shaykh Ibn Jibreen said: 

The purpose of sport is to train the body to move and become strong and healthy, and to become able to carry heavy objects and put up with hardship, because a person may need to rely on himself sometimes, and if he has physical strength he will be able to walk on his own two feet for a day or several days, and he will be able to carry his luggage and supplies and food on his head, and save himself from doom. It has happened that some people’s bus broke down in the desert and they were a day and night’s walk from the nearest town, and not one of them was able to save himself, so they all died, and there were about forty of them. Hence we think that governments should train their troops, workers and young people to walk and run and carry heavy objects, and to put up with hunger and the like. This is the benefit of sports and physical training, and this is what the sports player gets used to through training his body to move and bear hardship. But as for interviewing players and watching them on audio or video broadcasts or following news that is published about them, I think that this is not important, rather it is a waste of time and financial resources, and a blatant loss, because of the evils, envy, competition, travelling for long distances and great expense involved, in addition to the fact that it does not bring any benefit to the spectator, because when he goes to watch matches and buys a ticket, and he sits waiting and then watching for several hours, then at the end he is faced with the crowds and dangers, and there are sometimes traffic accidents and the like, all of that is evil and harmful and dangerous, which has no benefit. What benefit can he gain from watching these players and reading the newspapers that carry reports about them, and spending a lot of money on them and a lot of time reading them and following news of them.  

We advise the trainers and sportsmen to encourage the students of physical education to enter fields and competitions and to learn, and to warn them against wasting time on reading, listening and watching, or following news that is of no importance. Thus they will guide them to that which is beneficial and steer them away from that which is harmful. It is not permissible to praise the kuffaar if they become prominent in their field and excel in sports, rather we should compete in that which will benefit us in this world and in the Hereafter. And Allaah knows best. End quote.

Quoted from his website:

http://www.ibn-jebreen.com/book.php?cat=6&book=2&toc=71&page=66&subid=18502 

So there is nothing wrong with practising sport in moderation and adhering to Islamic etiquette, and there is nothing wrong with teaching that to others and training them. 

Thus we can see the difference between the sports analyst and the teacher of physical education. The analyst wastes his time and the time of others in things that are of no benefit, and his work may involve praising and venerating the kuffaar, which may attract the young to their ways and make them take them as an example. 

But the teacher of physical education is strengthening the bodies of his students, and they will benefit from that in both religious and worldly terms.

And Allaah knows best.