Why can't Montag call in that he's sick?

While discussing calling into work with Mildred, she is completely put off that Montag expects her to make the call to his boss. When she asks him why he can't call, we understand from his thoughts that he is afraid. He's afraid to call, and he knows if he speaks to Beatty himself...... he'll go into work when he shouldn't. His emotional state is going to raise a red flag, and Beatty is going to know what has been going on.

Because you're afraid, he thought. A child feigning illness, afraid to call because after a moment's discussion, the conversation would run so: "Yes, Captain, I feel better already. I'll be in at ten o'clock tonight."