One idea could be that the girlfriend, perhaps under the influence of an enemy, reveals Naruto's bloodline secrets to those who would use it against him. For example, she might be tricked into thinking she's helping Naruto in some way, but actually endangering him.
The ending of Girlfriend Girlfriend manga is quite complex and bittersweet. The characters go through various challenges and their relationships evolve in unexpected ways.
One possible reason could be that she was forced to betray him. Maybe an enemy got to her family and threatened her to turn on Naruto. For example, in the Naruto universe, there are many powerful villains who would stoop to such tactics.