Why did Robert want to run home after he and the movie on her birthday?

The most important piece of information is "on her birthday." This suggests that the reason for Robert's urgency is likely related to Alice's birthday celebration.

• A) He was very hungry and thirsty. This is a general reason for wanting to go home and doesn't specifically connect to Alice's birthday.
• B) He wanted to play with his friends. This is also a general reason and doesn't directly relate to the birthday context.
• C) He wanted to get away from Alice. This implies a negative sentiment, which is less likely to be the primary reason for "running home" after an activity on someone's birthday.
• D) He wanted Alice to get to her party. This option directly relates to "her birthday." It is common for people to have parties on their birthdays, and Robert's eagerness for Alice to get to her party (or perhaps for them both to get there) provides a strong, positive, and contextually relevant reason for him to "run home."

Based on the strong connection to "her birthday," option D is the most plausible reason for Robert wanting to run home.

The final answer is $\boxed{\text{D}}$