Generally, it is important that people practice what they preach, yet there are exceptions.
Conclusion
There are exceptions to the general rule that you should practice what you preach. rephrase: Sometimes its okay if you don't act in accordance with what they say.
Evidence (for instance)
Logicians don't need to be logical when they discuss logic, just like physicians don't have to be healthy to discuss health.
Evaluate
The author is trying to support the idea that sometimes it's okay if you don't practice what you preach. The evidence is an analogy, in which the author is assuming in both cases that it's okay if you don't practice what you preach.
It's okay for a doctor to tell her patient to stop smoking cigarettes, even though she herself hasn't been able to quit smoking.
It's okay for a logician to be discussing logic, even though they are being illogical as they do so.
Any time an argument is based on an Analogy, we should be asking ourselves whether the two things feel fair to compare.
In this case, it does seem perfectly fine for a doctor to treat my health conditions, even if they don't live a healthy lifestyle. But it doesn't seem as fine for a logician to be illogical while discussing logic. How will I emerge with a better understanding of logic, if the logician teaches it to me in some illogically?
To put it another way, what a physician does outside her clinic to her own body doesn't really affect how she treats people inside her clinic. The former is her life. The latter is her job.
But what a logician does within a discussion of logic seems like it is his job, not his life. If he can't be logical while discussing logic, then he's messing up being a logician.
Goal
Look for an answer complaining about the analogy, probably regarding the fact that while the physician example works for "you don't need to practice what you preach", the logician example seems weirder.