Justification of the used evaluation criteria , how to choose the evaluation criteria in classification task

I have used the training time and test classification rate as a criteria to evaluate my classifier ( as in many papers, many studies they used training test CR)

Is there anyone could explain why test CR and training time are the most used? Once we are asked to justify why these evaluation criteria, what a good answer should be? Honstly it starts to be a habit ( as in all papers I read) we asked how long the classifer does take? and the % of correct answer.. But I need more logical answers ( more explained...)