Haytham is against freedom, and wants the Templars to have complete control over the colonies/the world under a fake government headed by the man, Lee, who personally led the attack on Conner's village (and is an all around asshole). Conner tries to kill Lee, but gets attacked by Haytham. Haytham fights to the death with Conner in order to defend his conviction, same with Conner. Conner didn't want to kill his father, but he knew he had to in order to protect his people, and later, to protect the colonies. If Haytham only gave in, gave up his convictions, he would have been spared.
Which is why I liked his death speech, "Don't think I have any intention of caressing your cheek and saying I was wrong. I will not weep and wonder what might have been. I'm sure you understand. Still, I'm proud of you in a way. You have shown great conviction. Strength. Courage. All noble qualities... I should have killed you long ago."
They are both very similar, both strong, courageous, and have great conviction. The only difference is Haytham believed in order that came from a controlled society over the chaos of freedom, whereas Connor believed that everyone should be free, and that no one should have control over another.
I really like the story. It had a lot of murkiness when it comes to right and wrong, ends justifying the means and what have you. Both sides of the Revolution were wrong to the Native Americans, both sides enslaved and tried to control others. Conner and his tribe also were stuck between preemptive action to defend themselves, but not being able to withstand a counterattack (thus stuck between action and inaction). Connor was betrayed, and misled many times; but he still kept fighting for his cause, because he knew it was right. He knew he had to push forward and protect his people and everyone else who's freedom was at risk.