I do wonder how you would teach a subject in which you have no competence....for instance, how would I teach Trigonometry unless I had a working knowledge of the subject? In that case would I learn along with the kids?
The answer is: yes and no.
In the early grades, I've been amazed at how much I have learned right along with the children - especially in the area of world history. Really, my knowledge of world history was abominable! It's pretty good now, though. ;-D
Happily, homeschooling has become so mainstream, there are curriculums available covering almost anything you might want to teach. Some of these require a certain level of understanding of the subject by the teacher, but, especially at the higher levels, this is generally not the case. Extremely well written materials are available now, in which the students read and learn for themselves advanced subjects like trigonometry, calculus, physics, biology, chemistry, humanities/literature courses, etc. Students who have learned to read and comprehend well, and have acquired independent study habits, will be prepared for these courses when they reach the higher grade levels. Additionally, there are videos, classes on DVD, online courses, and many other learning options easily available.
In the big picture of life, knowing how to teach yourself - how to research, study, and find the answer when you get 'stuck' - may actually be the most useful academic skill you can learn.
Of course, there are some subjects which are difficult to study at home. Without a well equipped science lab, my children can only go so far in chemistry, for example. If we lived in the US, we could take advantage of many opportunities which have been created for homeschoolers. One very popular option is for homeschooled high school students to take courses such as biology and chemistry at the local community college. These students have the advantage of earning college credits while still in high school.
I feel certain we would be utilizing the community college option, if we lived in the states. If one of my children wishes to specialize in science, I may consider having them live in the US with a relative for a year, so that they would have this educational option. For now, we just try to balance this deficit by remembering how many educational opportunities the children have here (learning to speak fluent Spanish, and having intercultural experiences being two obvious examples) which they wouldn't likely have if we still lived in Maryland.
Really, the academic quality available through homeschooling has been proven over and over, as homeschooled students win education contests (spelling and geography bees, science competitions, etc) across the nation. These days, instead of homeschoolers finding it difficult to get into colleges, they find that they are quite actively recruited.
The more difficult topic to address is the question of socialization. Even as I wrote the paragraphs above, I thought of how lonely and boring it sounded, as if the homeschooled high school student sits alone at his desk, hour after hour, teaching himself out of huge tomes on difficult subjects. I will wait to discuss this question on another day, however. Right now, I need to go socialize my children!