I hope you have an explanation for being late because you cannot into the classroom until I hear it.
'Hear' is correct here. 'Listen to' would be very odd indeed.
When we 'listen to something,' we make an effort to hear it. We may even set aside from special time to listen to a concert, for example, or to listen to the radio -- things you do by choice. We also listen to someone when we want to know his/her thoughts.
In this case, you might think that the speaker wants to set aside time to give the student a fair hearing, but that's not exactly true. The speaker just wants to hear the noises that the explaining student will make.
If the speaker really wants to know the student's thoughts, the speaker will schedule an appointment with him to sit down and talk. At that talk, the speaker will listen to what the speaker has to say, and will have real interest in the student's words.
hear:listen to = see: watch
With 'hear' and 'see,' no effort is made. You can't avoid hearing traffic noise, explosions, unwanted loud music, etc. You hear the birds in the morning. Although you may like to hear the birds, you didn't choose to listen to the birds. You might choose to listen to bird songs, but if the birds wake you up in the morning, you hear them -- you aren't listening to them.
In the same way, you can't avoid seeing a sudden accident, seeing the trees when your eye wanders to the outside, seeing the smile on your mother's face when she sees you.
By contrast, you listen to music, by choice, and you listen to your favorite group, and you listen to your loved one's pleas for help. You don't just hear the music or your favorite group, and you don't just hear the pleas for help.
Similarly to listening, you watch your children, by choice, when they cross the street, you watch a football game, by choice, and the neurologist watches you while you walk and observes your behavior.
In the sentence in question, it may seem that the teacher should be listening to the student, and his excuse, but the teacher is not that friendly. The teacher just wants the appropriate words to appear, and is not going to waste any extra friendliness on this student.