Edmund himself voices his causes for complaint in a soliloquy in the opening of Act 1, Scene 2.
Thou, nature, art my goddess; to thy law
My services are bound. Wherefore should I
Stand in the plague of custom, and permit
The curiosity of nations to deprive me,
For that I am some twelve or fourteen moon-shines
Lag of a brother? Why bastard? wherefore base?
When my dimensions are as well compact,
My mind as generous, and my shape as true,
As honest madam's issue? Why brand they us
With base? with baseness? bastardy? base, base?
Who, in the lusty stealth of nature, take
More composition and fierce quality
Than doth, within a dull, stale, tired bed,
Go to the creating a whole tribe of fops,
Got 'tween asleep and wake? Well, then,
Legitimate Edgar, I must have your land:
Our father's love is to the bastard Edmund
As to the legitimate: fine word,--legitimate!
Well, my legitimate, if this letter speed,
And my invention thrive, Edmund the base
Shall top the legitimate. I grow; I prosper:
Now, gods, stand up for bastards!
He did not ask to be brought into the world. He had no say in the matter. He finds himself in a painful position because everyone knows he is illegitimate. In fact, in Act 1, Scene 1his father seems to be boasting about conceiving him. Gloucester seems indifferent to the feelings of his son who is standing right beside him. Gloucester seems more interested in portraying himelf as a sort of Don Juan or Casanova. It is no wonder that Edmund should have been building up a powerful head of resentment over the years and that it should finally result in a terrible reprisal against his father and his brother Edgar.
Edmund has to see Edgar every day, and he is continually reminded of the fact that Edgar is legitimate and heir to his father's title, lands, and fortune, while he himself has uncertain prospects. He may become dependent upon Edgar's charity, just as Orlando is utterly dependent upon that of his brother Oliver in Shakespeare's As You Like It.
Shakespeare had a genius for being able to see through the eyes of the characters he created and to write their dialogue from their points of view. Each character is understandable to the reader or viewer when seen from that character's own perspective. This even includes Goneril and Regan. Shakespeare identifies with all humanity. He understood that each of us is trapped inside his or her own mind and cannot help seeing himself or herself as the center of the universe--so important in fact that the entire universe will cease to exist with the cessation of one's own existence. This is to be noted in the death of the flunky Oswald in Act 4, Scene 6. He says to Edgar:
Slave, thou hast slain me: villain, take my purse:
If ever thou wilt thrive, bury my body;
And give the letters which thou find'st about me
To Edmund earl of Gloucester; seek him out
Upon the British party: O, untimely death!
Death is just as important a matter to Oswald, a nobody, as it is to Hamlet or King Lear or Macbeth--or to the viewer.
Edmund not only has legitimate cause for complaint, but he has a legitimate cause for hating his father and even some cause for hating his smug, secure, complacent brother Edgar. It might not be too far-fetched to compare Edmund to the monster in Mary Shelley's Frankenstein, who takes terrible revenge against his creator for bringing him into the world without his consent and causing him the torment of existing. We can dislike Edmund, but we are forced to understand him and even to admire him.