The half halt should not be ridden through the rein. It should be ridden through the rider's seat.
It is not intended to slow the horse down, when ridden and execute correctly. It's purpose is to rebalance the horse, by putting more weight on the hind legs, and therefore activating the hind legs.
To explain how to ride a half halt would take hours, days in fact, as there are so many versions on when to apply the aid, which aid should come first etc.
I ride half halts first with seat, then leg, then hand - the rein aid is merely a slight closure of the hand to contain the energy I have created in the hind legs, through the seat and leg aids. Definitely not a pull back on the rein. I also use both reins evenly to do this.
In training, rather than a test situation (dressage), I will apply the half halt, and as soon as I feel the hind legs activate and the forehand lighten, I ask for some extra flexion, or counter flexion, to test the connection to my rein. If your half halt was effective, there should be no resistance when asking for increased flexion.
Half halts are quite a delicate process and as you develop as a rider you find different and more effective ways of riding them. Some riders suggest riding the half halt through your lower leg, others say half halt at the base of your neck, ect. As you can see, its more complicated than just tugging on one rein to slow down!!