You got some really good answers. The other posts were just marelous and said everything I was thinking of saying.
(and yes, you do need to edit your posts to be sure that they are understandable. A few spelling errors are fine, but the message needs to be clear.)
Anyway, about becoming a better horseperson, I just wanted to add that you have already demonstrated the first requirement; wanting to learn more. So, keep an open mind and look to learn from whereever it may come. Ask questions when you can and let people show you things. You don't have to agree with them, but if you already think you know something you will have a closed mind and miss some good tidbit.
When I started taking dressage I had no idea what dressage even was. Never had even heard the word, "dressage". But I wanted to find someone who would just teach me good riding and harmony with the horse. So, that's how I felt when I went looking for an instructor. And the woman I ended up with , who taught me the foundation of dressage, though sometimes a royal b****tch, came from a place where the horse and his welfare are number 1, and that should be your number one prerequisite when YOU go looking for your instructor.
Now, as for a lead. At the canter the horse has a three phase stride.
To begin the canter, he starts on one rear foot. Let's say he starts on his right rear foot. That's phase one. Next he steps forward on his left rear and right front foot at exactly the same time ; phase two, and lastly, he reaches forward with his LEFT front foot, which is called his leading foot because it reaches a little farther in front of the other front foot. You know how a canter sounds like, "one , two ,threee .. one, two, three, . . One , two , three .. etc.) The "three" step is the leading step. After that step the horse has a moment of suspension where NO legs are touching the ground before the whole cycle starts over again.
When you canter to the left, you want the horse to be on the LEFT lead, for his balance. So, he needs to strike off with his right rear leg.
And for the right lead, it's the opposite.