Stepper Motor Pulses Making it reverse
You're skipping steps.

Full drive mode for a stepper looks like this:

 Step A  A' B  B'
  1   1  0  1  0
  2   1  0  0  1
  3   0  1  0  1
  4   0  1  1  0
  1   1  0  1  0


One of the A windings and one of the B windings are always on, and the rotor is resting halfway between the two powered windings.  This gives you maximum torque.

Half stepping sacrifices some torque to give you twice the resolution:

 Step  A  A' B  B'
  1    1  0  1  0
  1.5  1  0  0  0
  2    1  0  0  1
  2.5  0  0  0  1
  3    0  1  0  1
  3.5  0  1  0  0
  4    0  1  1  0
  4.5  0  0  1  0
  1    1  0  1  0


The half steps don't have as much torque, since only one winding is on part of the time.  But, the half steps are close to a full step, so it doesn't take much to get the rotor there.

You're skipping the full steps and just using the half steps.  You might also be sequencing the windings wrong.  I can't tell because your numbering scheme is atypical.

See a reference like this one for more information and pictures.