Debunking scientific paper "Has global warming already arrived?"
The comment is saying that the authors are making a fallacy as follows:

Temperature increase will be associated with an increase in tropopause height.
Using instrument/dataset X, we fail to measure a tropopause height increase.
Therefore, there is no temperature increase.

The fallacy here is that instrument/dataset X is not suitable to measure tropopause height, therefore one should not expect it can measure a tropopause height increase.
The comment is referring to the University of Alabama in Huntsville temperature dataset.  This is derived from satellite microwave temperature sounders¹.  From the Wikipedia article, this dataset provides:

UAH provide data on three broad levels of the atmosphere.

The Lower troposphere - TLT (originally called T2LT).
The mid troposphere - TMT
The lower stratosphere - TLS


The tropopause is the boundary between troposphere and stratosphere.  It can be defined in various ways, but to measure tropopause height you generally need to measure the temperature in the vicinity to the tropopause.  As this is apparently not provided by the dataset, it is impossible to use the dataset to measure tropopause height.

¹From personal experience, I can tell you that it is difficult to determine long-term temperature triends from satellite data.  Polar-orbiting satellites in sun-synchronous orbits experience a drift over time, which means that their local time ascending node changes; in lay terms, this means that when they previously always passed at 14:00 over a certain spot, 2 years later this may be at 16:00.  Even if that time wouldn't change, instruments degrade over time and get replaced by new instruments.  You need to be very careful to make sure you're detecting a trend in the temperature and not in the instrument itself!  I've worked on this in the FIDUCEO project, I was doing infrared temperature sounders and colleagues from Hamburg were doing microwave humidity sounders, but microwave temperature sounders were out of scope because none of us had the depth of expertise needed.  Even with the expertise, we underestimated the difficulty of the problem and ran out of time before we could properly declare we had delivered what had been promised to the funding agency, although we learned a lot.