Why is Theon Greyjoy so easily convinced to side with his family and go against the Starks, even though he has been emotionally connected to them through all these years? Knowing only the TV show, such behaviour seems a little bit "jumpy".
My view is that I don't think he is easily convinced as such - but instead arrives at his most of his actions through a combination of emotion (that overrides reason), a sense of entitlement and his own selfish desires. His character is motivated primarily by bis own pride and ambition as the heir apparent of the Iron Islands. But just as importantly, he is ignorant of his own people (the Ironborn) and The Old Ways by which they live. This is clearly shown by the scene in which Theon meets his father for the first time since he was taken away to live with the Starks; Balon is disgusted by what his son has become - he denigrates Theon for wearing gold jewellery that he has not paid "the Iron Price" for (i.e. seized by force/stolen). At this point, Balon essentially disinherited his son and wanted nothing to do with him. This ignorances pay a key part in the mistakes that Theon makes.
This is because Theon's upbringing with the Starks has instilled in him different values to the Ironborn, as such he not only does not follow the Old Ways but also believes firmly in his right by birth to rule the Iron Islands, an idyllic notion which does not reflect the harsh realities of life away from the mainlands. Confused by his father's repudiation of his only surviving son, Theon endeavours to prove himself and win back his favour in the only way he knows how - working against the Starks. The tragedy of Theon's situation is that he fails to see the consequences of his actions - that he has little to gain, and everything to lose - and as such sets himself down a path that can only bring him sorrow through the destruction of the North (which he feels conflicted about - as although his hosts may never have loved him, he is dimly aware that they did treat him well, and indeed he later has trouble with the idea of harming his foster brothers precisely because of this reason) and no joy, for the people of the Iron Islands do not (and cannot, given Theon's years as a hostage) respect him and he can never hope to overcome the obstacles to his fulfilling what he sees as his right to rule them.
As such, although Theon does despicable things, and his pride and selfishness is his downfall, it is not too hard to feel sorry for him in my opinion. As I say his situation is very tragic, his problems stemming largely from his conflicted emotions rather than any sense of cold cunning or reasoned planning, which sets him apart from most of the other villains of the series as I see it.
Theon has always thought of himself as the only possible heir of the Iron Islands, and this explains a little bit his arrogance. Now when he finally gets to meet his father for the first time since he was taken by Ned Stark, he understands that:
- his father despises him because he is sent by Robb Stark, who he considers his enemy
- he doesn't live by The Old Ways, which is the Ironborn tradition (for example he bought his cloak instead of taking it from an enemy's dead body)
- his sister is likely to be the heir (to his eyes, she is basically stealing what he always considered his own by right)
So he is ready to do anything to prove himself worthy. His growing up with the Starks has altered his values: he thinks he can claim the throne of his father only because he is the only living son, but for an Ironborn, everything has to be earned with the Iron price. When he comes back to the Iron Islands, these old values resurface.
Although Theon has been raised with the Starks, only Robb treated him nicely (I mean, almost like a brother). He later admits that (Season 3 spoiler, so probably ASOS spoiler)
he hates the Starks because they took him from his father.
And after all, he is just trying to please his family
Now you may think that this is not enough to betray a family that almost raised you your entire life, but actually, they did not: they just hosted him and didn't treat him at all like he was a Stark.
So he had a choice: betray the Starks, and try to win his father's throne later (just like the former rebellion, his father wants to be King of the Iron Islands), or staying with the Starks, and stay in the King in the North's shadow forever. Remember, he is arrogant.
Hope this helps