x| |x
|o|
o| |x
I have a fork on top row and right column, so win.
But actually, your first move was correct, and you can defend my second move.
Go for an edge square, for example
X|o|
|o|
| |x
Then I have to defend your two-in-a-row
x|o|
|o|
|x|x
Then you have to defend my two-in-a-row
x|o|
|o|
o|x|x
Then I have to defend your two-in-a-row
x|o|x
|o|
o|x|x
And you defend my two-in-a-row
x|o|x
|o|o
o|x|x
And I have the last move with only one option left, so a draw
With the corner strategy, there is only one correct way to defend it, which is why I go for it.
If you go for edge as your first move
x|o|
| |
| |
I go for bottom left corner, You defend it, I go for the other corner, and get a fork (two possible winning lines)
If you go for adjacent corner as your first move
x| |o
| |
| |
I pick one of the other corners to get a fork
If you go for opposite corner as your first move
x| |
| |
| |o
I pick one of the other corners for the same possibility of a fork.
I worked this out for myself while in primary school. Lots of other people have worked this out too.