I think the claim that Earth is going to turn into Venus or Arrakis is absurd - I haven't heard anyone argue that, but I have heard the claim that it will cause a mass extinction on a geologic scale that could affect humans and our 'pets' as well.
I don't know if it is accurate and based on good science, but I believe that the argument revolves around the timescale that the change is occurring compared to natural climate shifts: that the temperature is increasing so fast there is not enough time for plants and animals to evolve, or even for ecosystems to gradually migrate their locales.
For example, one reason you can't simply replace farms with land in, say, the Canadian shield is the lack of good topsoil. According to [1] it takes at least 100 years to form an inch of topsoil in wet, hot climates, and the process is much slower in cold or dry climates. Thus if we render our existing farmland unfit for our existing crops in timescales measured in tens of years, we would have to rely on manually bringing a literal continent's worth of soil north - whatever process was at work during the Cretaceous cannot be relied on to solve this particular problem.
[1] https://www.nrcs.usda.gov/wps/portal/nrcs/detail/wa/soils/?c...