Albert felt that he should seize this opportunity to have a proper chat with Dumbledore, and by the way, find a way to get the Headmaster to clear up some of his doubts.
In the past, he hadn't wanted too much contact with Dumbledore, entirely because his Occlumency skills weren't high enough, and he didn't want to expose his magical attainments prematurely. But now things were different; he was of age and had won numerous international awards. Presumably, Dumbledore already had some understanding of him and harbored no malicious intent, so he believed the two sides could have a good communication.
Of course, the most important thing was that in a few years Dumbledore might die.
Chapter 798