I did the 3rd Gym, and came to veridian city, but now the old man in the exit of the city, dont let me go out. Dont know why =l, I go to school like he tell me, but i cant fight with Jackson.

did u try to talk to jackson mom?

If you fight with Jackson and lost, you have to got back to start town and talk to his mom; then go back to the school, where Jackson will be dragged out by his mom in order for you to progress through the game.