The harder she clings the more she pushes him away. Eren is a kindred spirit like a bird, you can't try to force him to stay with you, you have to let him go. And who knows sometimes that bird might just come back to you.
Eren can use the 3dmg too, every military has to know how to use it (otherwise they wouldn't be able to fight titans at all), but as you saw by episode 7 (7,8, I dont remember) he "died". Mikasa is just abnormally good with this equipment, like Levi.
He died because he saw a friend dying. He got so full of rage that he lost his mind and went with all his will to slaughter that titan.... But he is not like that anymore, he matured and is learning to control his emotions, which he learned in the hard way