Why is electric field due to negative charge directed towards itself?
To consideration for the direction of electric field line from positive end to the negative is related to the experiment in which the unit coulomb positive charge is placed near the charges to determine the magnitude and direction of its movement. The direction of the electric field is always directed in the direction that a positive test charge would be pushed or pulled if placed in the space surrounding the source charge.
So as this unit positive charge would be repel by the positive charge and attracted by negative one . The electric field line when traced would be from positive to the negative.