Just prior to
killing his father, Han Solo
Kylo Ren says that he has to do something difficult (paraphrasing).
Is there more to it other than the simple fact that his father is part of the rebellion?
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In parts of the film we see Kylo Ren struggling to stay on the Dark side. He confesses this to Snoke and Snoke also has worries about whether or not Ren will be able to kill his father. Ren is also seen confessing the issue of the Light side to the melted helmet of Darth Vader.
He kills his father as a way to strengthen his resolve, a reinforcement of his testament to the Dark side of the force. I think in part he also believes this will make Snoke believe in his resolve as well.
The reasons then are ones that are often seen in Dark side users selfishness and power hungry-ness. These two motivations will also help to solidify his stance on the Dark side at least within his own internal struggle.
I'd also doubt the rebellion part has much to do with it anyway, until a few days prior Han was not even associated with the new rebellion except through Leia.