Negi's strengths are his intelligence and motivation to succeed.
Rakan's and Negi's fight is a typical Master vs. Student battle. Kagetario and Kotario are going to have a good fight, too. Kagetario had proven himself to be a good fighter. Rakan is still strong fighter who will not to be easily worn down. Rakan's strength is his experience as a fighter. Negi's major strength is his youth.
... Only reason I can think of is to test the son of his eternal rival, Nagi. He's too lazy to want to find and fight Fate himself, I'd say, so training Negi is the next best thing (reason 2?)
In a way, Rakan is proven to have two reasons for entering the tournament. One of his reasons is to make sure that his student Negi doesn't have an easy fight at the finals. Rakan wants Negi/Nagi to work for his victory.