First, a woman asked him whether she could postpone the fast to the following day, Friday. She She needed to ride to a meeting with a noble on Thursday, and fasting that day would be extremely difficult. Rashi responded that, though it is not a normal public fast day, it is nevertheless a communal custom, and therefore one should not break away from the community and observe a different date. Unclear what the woman should do - perhaps it was better that she not fast at all than that she observe the fast on her own date.
Second, he turned his guns on the "prushim", zealots, who would fast on both Thursday and Friday. About them, Rashi would invoke the verse "And the fool shall walk in darkness". They did not retain the proper distinction between biblically ordained commandments and customs. Most people observe the fast on Thursday, and that's good enough.