The passage quoted seems intended to mock the teachers for their lack of enthusiasm for the author's idea. The teachers were tired and cynical, so that partly explains their lack of enthusiasm.
The opening phrase "I can still remember the faces" draws us in to the comical absurdity of the teachers' reaction to the author's idea.
It is, of course, a ridiculous exaggeration to say the teachers reacted with horror, but that is the author's point. The teachers reaction was laughably overblown.
The word "pet" here means, I think, "favourite" and implies that the teachers actually enjoy raising objections to the author's idea. Here, it does not, I think, denote that the teachers strongly objected, but rather that it ws something they enjoyed objecting to.
Many people do have subjects they seem to enjoy complaining about, such as the fact it always rains on Sundays and public holidays. They are not genuinely furious about it, they don't expect anything to be done about it, they don't even really believe it: they just have something they seem to enjoy moaning about.
Here the author is saying that the teachers' objections were grotesquely overblown, but also they were not serious. They just enjoy moaning about extended reading.
If the teachers had been less tired and cynical, if they had not enjoyed being awkward, then they would, of course, have been more receptive to the author's idea.
The attitude expressed by the author is not uncommon amongst management consultants, but of course that doesn't mean he was right. The teachers may have had perfectly good reasons, well articulated by abbie, but to understand the passage here we have to recognise the insidious nature of the author's intent.