Electric field inside a sphere of charge

[maccha]

So I understand that to find the electric field inside a sphere of charge you can use Gauss's Law by drawing a sphere inside, enclosing the charge. But, intuitively, I don't understand it.. why don't the charges outside this sphere contribute to the electric field? I know the total flux through the sphere you've drawn will be zero, but I don't know, it just doesn't make sense visually to me.

 

[Redbelly98]

The fields due to the charges outside the sphere all point in different directions. The vector sum of these fields, as it turns out, adds up to zero.