Disclaimer: Didn't, couldn't, and wouldn't own Naruto.
The Reasons Why
Hiashi was never really considered a kind man by anybody. Calculating, cold, and arrogant, yes, but he was not kind. So when he stood, stoic and proud while his eldest daughter paled in shock, sadness, and anger, no one was surprised. And even less surprising was Hiashi's retreating back while his nephew, whom he had trained and housed as his own son for eight years, narrowed his eyes in anger and hatred.
For he had destroyed their lives – he had taken away their freedoms and futures. He had ordered them to marry each other.
But it was because Hiashi loved his clan that he did this. He knew that his clan needed the image of a strong leader who was not afraid of his own shadow. He knew that clan pride demanded that they be led by none other than the strongest of Konoha. He knew that the clan would benefit from the healing and the mixing of the two branches that would be brought on by the marriage of Hyuuga Neji and Hyuuga Hinata.
He did not care that he would crush the hearts of both Tenten and Naruto who had come to love Neji and Hinata, respectively, deeply and wholly. They were outside of the clan and therefore beyond his notice. He did not care that Neji nearly killed his daughter eight years ago in a fit of hatred and anger and resentment. Those feelings were misplaced after all, and were to be buried in the past. He did not care that Hinata still held onto a little of her fear of her cousin in spite of having forgiven him for his actions. A little fear was healthy in a marriage, naturally.
He ignored the fact that Hinata and Neji would also have their hearts crushed alongside those of their lovers. It is always best for ninjas not to be clouded by emotions. He ignored the fact that these two did not love each other the way spouses should love each other. Love was never important anyway. He ignored the fact that they would likely resent him for the rest of their lives. As long as they were married, what did he have anything to do with it?
But he could be bothered with the notion that their anger with him might interfere with the running of the clan. It wouldn't do for them neglect their duties. He could be bothered that they might never learn to tolerate each other enough to produce an heir. Hinata just couldn't afford to fail again. He could be bothered with the idea that they may never learn to accept their fate. Fate was not something that should be fought against. It would be a tiresome endeavor. But he would not be bothered with anything nearly enough to change his mind.
Because Hiashi believed that Hinata could and would bring light to the Hyuuga clan. Because Hiashi knew that for her to fulfill that role, she needed to stay within the clan and not marry out. Because Hiashi foresaw that Hinata weak and meek as she was and Neji, harsh and proud as he was, would learn from each other and grow to be such wonderful leaders, the both of them.
But mostly because Hiashi loved both Hinata and Neji very much, and knew it was worth the temporary pain in his heart caused by their hatred of him, to know them to be both secure in the future.