7 Reasons Why Robb Stark lose the War
The War of the Five Kings erupted after the death of King Robert I Baratheon and the imprisonment of Lord Eddard Stark, whom eventually beheaded by Robert's heir, Joffrey Baratheon. Ned Stark, the Hand of the King at that time discovered the true parentage of the King's children, that they are a product of incest between the King's wife, Cersei Lannister and her twin and member of the Kingsguard Jaime Lannister.
Eddard Stark was supposed to tell the King but is outmaneuvered by the Queen and her allies, and was imprisoned. Robb Stark after hearing the news, called his bannermen and declared war against the Lannisters.
Robb Stark won every battle against his adversaries, yet failed to save his father and two sisters, Sansa and Arya. After his father's death he is then called, the King in the North and continued to push Lannister army back, almost winning the war. But then, things happened against the King in the North, that made him lose the war, his life and his dream to give justice for his father.
Bad decisions, internal affairs and mindful opponents defeated the North King, not battles.
As of 'A Dance with Dragons' and Season 5 on the TV Adaptation, House Stark is on exile and its family all separated from each other.
1. He broke his vow and married Jeyne Westerling
Riverrun, Catelyn Stark's homeland is under siege by the Lannisters and must be repelled by the Stark's forces. But first they have to cross the Twins, a bridge to the other side going to Riverrun. Unfortunately, it is manage by the wicked Lord Walder Frey who don't want to support the Starks and draw the bridge for them, even if he is a vassal of the Tullys. Lady Catelyn managed to talk Walder into submission by arranging her daughter Arya Stark to one of his sons and Robb to one of Walder's daughter. Furthermore, the Frey troops joined the North and Riverlands army against the Lannisters. Robb successfully crossed the bridge and lifted the siege at Riverrun.
At the end of the war, Robb, the Young Wolf, must marry the Frey girl because of the agreement, even he don't agree with it. Yet, as a saying goes, a young man's heart is fragile. The book and the television series has different story and character about Robb's lover.In the book, her name is Jeyne Westerling, the eldest daughter of Lord Gawen Westerling and Lady Sybell Spicer. Robb was injured during the attack on the Crag and learned of his brothers fate, Bran and Rickon, who presumably died at Winterfell. Jeyne comforted him making the King in the North fell in love with her. Robb impregnated her, and in order to preserve her honor and his, they wed together.
At the television series, Jeyne is named Talisa Maegyr, a healer from a noble house in Volantis. Robb met her after a battle and had romantic relationship
Walder Frey learned of the King's breaking of oath and pulled out his army. Robb is then killed during the wedding of Edmure Tully and one of Frey's daughters, orchestrated by Walder, Lord Roose Bolton and Tywin Lannister. The Stark army, losing a king, went into turmoil and forcibly bowed to their Liege Lord, the Boltons and to the Iron Throne.
The breaking of oath of Robb Stark is the major turn of event of the War, and as Jaime said, Jeyne/Talisa is not a beauty to lose a kingdom for.
2. Edmure Tully's Tactical Blunder
Robb Stark and his bannermen were supposed to trap Tywin Lannister in the riverlands, but Edmure Tully, the Lord Paramount of the Trident, "successfully" defended the crossing, pushing back the Lannister army, thwarting Robb's plan.
This delay gave Tywin Lannister the chance to regroup with the Tyrells from the Reach and counter-attack the assault on King's Landing by Stannis Baratheon. The combined forces of Casterly Rock and the Reach rescued Joffrey on time and giving Robb's enemies a fresh start.
Suppose that Edmure Tully allowed the passage of the Lannister forces to the riverlands, they will be trapped and flanked by the Northern Forces and Riverlands cavalry, not giving them opportunity to help King's Landing against the Baratheon forces. Eventually, Stannis would surely execute all Lannisters and their allies and sit himself on the Iron Throne, giving justice to Eddard Stark and relieving Robb of one of his sworn enemies.
3. Sending out Theon Greyjoy
One of the most foolish act of Robb Stark is sending back Theon Greyjoy to his father in Pyke, Lord Balon of House Greyjoy. Theon became a hostage of Eddard Stark at a young age after his father, Balon, was defeated on his failed rebellion. Balon other two sons had died and his only remaining son, Theon was captured and grew at Winterfell, miles away from Pyke, so his father won't attempt the rebellion again. Obviously, Balon still has resentment towards the Starks and the Crown.
Theon Greyjoy was send to Pyke by Robb Stark to negotiate with his father in joining the Northern Armies with defeating the Lannisters, in exchange of looting the South and independence from the Iron Throne.
Balon didn't welcome his son warmly, but resented him for being too long gone and loyal to the Starks and seemingly forgetting his Ironborn norm. He also didn't accept Robb Stark's terms since he has other bigger plan, pillaging the North. In order to regain his father and subordinate's trust, and reclaim his place with the Ironborn, Theon once again joined his house, betraying Robb and attacking Winterfell.
With Winterfell under the hands of Theon, Robb had to pull back from his invasion of the Westerlands to redeem his family's castle. If he didn't send out Theon, Winterfell would still be free (The Greyjoys won't capture Winterfell because it's far out from the sea), Theon would still be his sworn brother and proceed with his invasion of the Westerlands, crippling badly the Lannister forces.
4. Executing Rickard Karstark
House Karstark is one of Robb's vassal and one of the most powerful. Rickard Karstark was the Lord and was executed by beheading of Robb because he killed two Lannister kids being held hostage. This was after the Kingslayer, Jaime Lannister is freed by Catelyn Stark as an exchange for her daughters held hostage at King's Landing. Karstark want the Kingslayer dead for killing his sons but took that chance from him, so he killed the other Lannister children.
Destroying his honor and justice, Robb Stark is quick to act and beheaded Lord Rickard Karstark as punishment. Followed by Karstark troops leaving Robb, this really triggered the infighting and disloyalty among the Northern army.
5. Death of Renly Baratheon
Lord Renly Baratheon of Storm's End, King Robert's youngest brother proclaimed himself King and rightful heir of the Iron Throne, with the support of Storm's End and the Tyrells at his back, as he is betrothed to Margaery Tyrell.
He reasoned that Westerosi people don't love his elder brother and rightful heir by succession, Stannis, and he will be a much better King. So he took up arms and willing to crush his own brother's forces. Lady Catelyn Stark proposes that Renly and Stannis join as brothers to fight their common enemy, the Lannisters, yet both are stubborn and lusting for war against each other.
However, King Renly promises Catelyn Stark that he is willing to help Robb with defeating the Lannisters, right after he crush his brother's army. He even said that the Young Wolf can continue to reign as King in the North even after he sit on the Iron Throne, giving them independence. But right before the alliance come to terms, Renly Baratheon is murdered by a shadowy figure came from the womb of Melisandre, Stannis Baratheon's red priestess.
If ever Renly lived and defeated Stannis with his 100,000 men, there'll be no chance for the Lannisters to win the war, except if they think of greater deadly schemes, a feat of Tywin Lannister. Nevertheless, the war would be shorter and there's a higher possibility for King's Landing and House Lannister to, just surrender.
6. He didn't kneel to Stannis Baratheon
Right after Robert died and the discovery of Joffrey and his sibling's true parentage, Eddard Stark, then Hand of the King, wrote a letter proclaiming and supporting Stannis Baratheon, as the rightful heir, not the bastard Joffrey. This act killed him though, yet Stannis knew it all, that he is the heir, and Robert's children is not his children.
Stannis, a seasoned commander, raised his forces, all that he can muster from Dragonstone and his wife's house, House Florent. It isn't large and his brother in the Reach is hindering him to conquer King's Landing and sit his ass on the throne. The deadliest weapon Stannis has is Melisandre, whom killed Renly.
Robb knew Stannis is the rightful king, so he didn't had better reason to be independent and declare himself another ruler. If I were Robb, I would take up the cause of Stannis, join forces with him and take the Iron Throne for the legitimate King.
7. Robb did not secure his vassal's loyalty
Robb broke his oath, by marrying another girl and Walder Frey took this as an insult. Rickard Karstark is executed for killing Lannister children, wherein the Lannisters are their enemies. The loyalty of his men wavered even though they won almost all battles.
As a king during a war, you should protect your bannermen's loyalty in order to continuously gain their support for your cause. Robb acted too much a king, a man of honor like Ned, forgot they are on a war and not all wars are won by swords.
Tywin Lannister, aware of what's happening between the Northern army, secretly negotiated with Walder Frey and Roose Bolton. Roose will be Warden of the North after the Starks are defeated, a very appealing offer, and a demand Roose is willing to do.
With the Freys, they orchestrated a plot to kill Robb and his loyalists. They use the wedding of Edmure Tully and Roslin Frey to purge most of the Northern Army. Here they managed to assassinate Robb and Catelyn Stark. The Red Wedding ultimately determined the outcome of the war between House Stark and House Lannister, and greatly influence the War of the Five Kings, with only Joffrey Baratheon and Stannis Baratheon contending for the throne.