That Rama killed Vaali in an unfair manner cannot be disputed for reasons like:
- Vaali didn't have personal enmity with Rama.
- Rules of human society cannot be applied to the animal kingdom (my personal belief is that those called as monkeys were primitive humans who resembled apes. I don't accept that humans talked with monkeys, bears etc. The story of Ramayana has to be understood metaphorically and not literally).
- Two persons (Rama and Sugreeva) fighting a single one (Vaali) is unethical by the code of conduct that existed during that time.
- Killing someone from behind is also wrong according to that time.
There may be many other valid accusations. There can be many equally valid justifications but one explanation stands out and it is not based on the virtue of Rama but of Seetha Rama.
While Rama can be regarded as the epitome of manly strength, Seetha was an embodiment of pure love. It is not as if Rama wasn't capable of love; it's just that some of the love had to be traded-off for strength. So, when Ravana abducted the compassionate Seetha, Rama became incomplete and violent without her gentle presence nearby to calm His anger and forgive the offenders. How can there be justice or mercy in a world where the goddess of compassion, Seetha Herself, has been abducted? Without Seetha, Rama was not His usual self and He lost His patience. He became Aniruddha (the Unstoppable One) and everyone standing on His way to reclaim His beloved was run over.
It is not 100% possible to support a comment in a text like Ramayana because it has to be felt from the heart than read from the brain. Also, since this text comes as a tradition from a very ancient period, there may not be an absolute proof other than what has been conveyed through tradition to those who have been fortunate enough to be at a listening distance.
From Valmiki Ramayana, Aranya Kanda (3.66). Note especially 3.66.18 The importance of having a compassionate woman like Seetha not only applies to Rama but also to all husbands. Power alone cannot help. Only a power that is accompanied by love can be constructive and help save the world.
1 & 2. Lakshmana, son of Sumitra, consoling the mighty miserable Rama, who was afflicted with sorrow, and was weeping helplessly like an orphan, drowned in great delusion, devoid of consciousness, pressed his feet and addressed him:
3. O Rama, king Dasaratha begot you by doing a great penance and performing great deeds, just as gods begot the nectar.
4. King Dasaratha, impelled by your virtues, and (unable to bear the) separation from you attained godhood as heard from Bharata.
5. O Rama, if you cannot bear this sorrow that has befallen you, how can weak and ordinary persons endure (such suffering)?
6. O best of men, if you grieve and burn the world with your brilliance, wherefrom will the (ordinary) afflicted people get relief?
7. It is the go of the world. Yayati, son of Nahusa, shared heaven with Indra but because of his curse (for his bad conduct) suffered misfortune.
8. To sage Vasistha, our father's priest, were born a hundred sons in a day.But all of them were killed in one day the same way.
9. You (rigidly) adhere to truth.(Like you) the mother earth who is adored by all the worlds, is unshakeable. Yet she is seen to be shaking at times.
10. The powerful Sun and Moon, righteous entities, who are the two eyes of these worlds and on whom everything rests firmly, also suffer eclipses sometimes.
11. O best among men, fate spares none. Great beings, every creature, even the gods cannot escape fate.
12. I heard that Indra and other deities are also governed by the principle of justice. Therefore, you should not bewail, O tiger among men.
13. Even if Vaidehi (another name of Seetha) is killed or abducted, you should not grieve like ordinary men, O sinless hero.
14. O Rama, you always see the truth. So, in the face of great difficulties men like you, whose vision is not blurred, should not lose heart.
15. O best among men, judge the facts rightly with your intellect. The wise apply their minds and know what is right and what is wrong.
16. Good results are not expected from the actions of persons who cannot distinguish between their virtues and vices, from those who are unstable in their deeds.
17. O Rama, you yourself in the past have instructed me many times that way. Who can be your adviser in this matter ? You are indeed like Brihaspati (the Guru of Gods).
18. Even gods cannot fathom your intellect. I am only trying to rouse your wisdom your sorrow has sent to sleep.
19. O bull among the Ikshvakus, weigh your divine and human prowess before you try to kill your enemies.
20. O best among men, where is the good in the destruction of all? Know your sinful enemy before you uproot him.
From Valmiki Ramayana, Yuddha Kandam (6.113) The mercy of Seetha.
Thereafter, having joined his hands together in salutation, standing in front of Seetha in humility and free from flurry, Hanuman again spoke to Seetha (as follows):
"If you permit me, I wish to kill all of these notorious female-demons, by whom you have been frightened earlier.
"These cruel female-demons of terrific form and behavior, with still more cruel eyes, having ugly faces, were heard by me here speaking again and again harsh words to you, who are so devoted to your husband, at Ravana’s command, when you were suffering hardships in the Ashoka grove, O divine lady!
"I wish to kill with various kinds of strokes, these cruel, extremely rough and deformed female-demons, with distorted features and terrific hairs and eyes, talking together roughly. (Pray) grant this boon to me.
"I wish to kill the female-demons, who have spoken harsh words to you and wronged you, striking them down with my fists, hand-blows, long arms, blows of my shanks and knees, by causing pain to their teeth, biting off their ears and nose and pulling out their hair, making them severely dry-mouthed, tearing them off, leaping over them, encountering them and throwing down their bodies, with their burst cheeks, necks, shoulders and ribs.
"O illustrious lady! Striking them with several blows in this way, I would destroy the female-demons of terrible form, by whom you have been threatened in the past."
Reflecting as pondering for a while, when spoken thus by Hanuman, the compassionate Seetha, who was kind to the miserable, spoke to Hanuman as follows:
"O the foremost of monkeys! Who will be angry with servant-maids, who are dependent on their king’s command and work in obedience to the orders of others?
"All this is reaped by me, as a consequence of my bad fortune or an account of a misdeed committed by me in the past. The fruit of one’s own making is indeed experienced (in one’s life).
"O the great-armed Hanuman! Do not speak like this. This is indeed a great divine strategy. It was ordained that this type of situation is to be obtained by me, due to the application of fate. Feeble as I am in these matters, I am forgiving the servant-maids of Ravana here.
"O Hanuman! As commanded by Ravana they threatened me. As he is dead now, they will not do the threatening.
"O Hanuman! There is an old maxim possessed of merit, actually uttered by a bear in the presence of a tiger. Hear it from me:
"'A superior being does not render evil for evil, this is a maxim one should observe; the ornament of virtuous persons is their conduct.'
"One should never harm the wicked or the good or even criminals meriting death.
"A noble soul will ever exercise compassion even towards those who enjoy injuring others or those of cruel deeds when they are actually committing them. Who is without fault?"
Hearing the words of Seetha, Hanuman who was skilled in speech, then replied to the faultless Seetha, Rama’s consort (as follows):
"O divine lady! You are the apt wife of Rama, full of virtue. Give me a message in return. I will go to the place where Rama is."