1. Public Speaking. I imagine life as a teacher would suck if you found public speaking challenging, it's what the majority of the day is spent doing! You have to be comfortable being in front of a group who listen to your every word. Assemblies, parents evenings, and staff meetings can all add different types of public speaking into the mix too.
2. Working Under Pressure. Teaching involves a lot of constant pressure to perform. Primary teachers in particular don't get much down time. You may get in at 7:30, prep all your lessons or mark books, teach an hour of English, an hour of Maths, and then having to go and do break duty. Straight into a science lesson, and then 45 mins to go and get lunch (and prep for afternoon). Repeat for the two or three lessons in the afternoon. Throw in a meeting with the deputy after school, and 30 books to mark for each lesson taught that day. Oh and then a planning meeting for all the lessons next week. You don't get much time to breathe!
3. Creativity. Teachers in the UK (it was noteably different in the US) are expected to recreate the wheel with each lesson. Its frowned upon to just follow a plan, and you're rather bizarrely credited for teaching in a new and different way from everyone else. The government may well publish a lesson plan but god forbid you just teach it from that. We also have to decorate the classroom walls, and change them regularly. You also get walls assigned to you around the school. It is no longer acceptable to just staple some children's work up.
4. Improvising with ease. Supply teachers should be especially good at this one, but all teachers will be required to think on their feet. A lesson may not go as planned, you may suddenly have 30 children staring up at you, and the planned activity is no longer possible. Or a session finished earlier than planned and you've got ten minutes to fill. Or its raining and you can no longer do the PE session outside.
5. Being able to explain something to someone who doesn't understand it easily. The actual ability to teach someone something isn't as common in teaching as it perhaps should be! We can all remember a secondary school teacher who was super clever but couldn't actually teach us much. A good teacher is able to step into the view point of someone else, and start from there, rather than expecting the world to see everything as they do themselves.
6. Being in charge. Primary teachers are often rulers of their own kingdoms. When that classroom door is shut, and you have 30 children who look to you for all direction, you have to become comfortable with that level of power. What you say tends to be fact. There isn't usually time for debates, explanations or discussions. I remember finding parent evenings particularly challenging in this respect. You're now in the role of 'teacher' and are all grown up and responsible....apparently.
7. Learning things quickly. If you're a primary teacher you end up having to teach everything. Science, PE, RE, art, maths, etc etc. Its a lot of knowledge to acquire (and yes its more in depth than when you were at school!).
8. Managing children that are more challenging than most. I've taught children who had an actual fight 90% of the time they were allowed to play outside. I've taught children who regularly throw chairs across a full classroom, children who crawl under coats in the corner when they are asked to write a sentence, children who have bitten me, and children who have been unable to write a basic sentence while their classmates are doing long mulitiplication. I've taught children who come from very sad homes, who are unable to communicate their own sadnesses in any other way apart from agression. It's pretty eye opening. These sad and angry children tend to become sad and angry adults.
9. Learning to play the game. I think that sadly, good teachers, need to be good at playing the game. I also believe that most industries have similar games to be played. Within a school you have the rules the goverment set, the rules the local council set, the rules of the head teacher, the rules of your head of department and the rules you set in your own classroom. It's highly unlikely that these rules will be the same. What is crucial is being able to work out what must be followed, what can be bent slightly, and what can be completely forgotten.
10. Making decisions. I sometimes forget that there are people who find it very hard to make a decision. Teachers naturally have to make decisions constantly, and as an only child it's something I've never struggled with. I imagine that with siblings, it would be possible to not make as many decisions, as your sister or brother may make them for you. I'm not saying that strong decision makers are always a better thing, just that it is a skill teachers are good at (whether naturally or acquired).
I'd love to hear about the transferrable skills you have developed in your own job (past or present!)