How did plants adapt to $\small\sf{CO_2}$ levels past 400k years? Why won't they do it again?
I'm not sure where and why has all CO2 gone every 100.000 years and out of where has CO2 come?


The amount of CO2 in the atmosphere for the last 400000 years is very strongly correlated with temperature.


Temperature change (blue) and carbon dioxide change (red) observed in ice core records.
Image source: https://www.ncdc.noaa.gov/paleo/globalwarming/temperature-change.html.


Glaciations currently occur at roughly one hundred thousand year intervals, driven primarily by Milankovitch cycles. So what causes the strong correlation between temperature and carbon dioxide levels? The primary reason for this marked correlation is that carbon dioxide dissolves in cold water much more readily than it does in warm water.

As a glacial period starts, the oceans gradually get colder worldwide as ice gradually spreads over the Northern Hemisphere. This enables oceans to absorb carbon dioxide from the atmosphere. Atmospheric CO2 drop as a glaciation proceeds. The plot shows that both temperature and CO2 levels drop rather slowly over the course of a glaciation, and then both rise rather quickly as the glaciation ends.

One reason for this is atmospheric carbon dioxide levels. The Milankovitch cycles triggers the end of a glaciation. The warming oceans cannot hold as much carbon dioxide as they could during the depths of the glaciation and release carbon dioxide to the atmosphere. This exacerbates the warming, releasing even more carbon dioxide into the atmosphere. This makes the escape from a glaciation much steeper than the entry into one (Shakun 2012). A nice graph from the cited paper:


Upper plot: CO&#x2082; concentration (yellow circles), global temperature (blue), and Antarctic temperature (red).
Lower plot: Simulation results that show that Southern Hemisphere temperatures tends to lead but global temperatures tend to lag CO&#x2082; levels.
Image source: http://www.nature.com/nature/journal/v484/n7392/fig_tab/nature10915_F2.html.


  But if CO2 came from burning trees or volcanoes and disappeared because plants adapted then I have this question:
  
  Plants somehow tolerated these 100.000 year CO2 changes over time which is very evolutionary small time. So perhaps adaptation was just about changing plants' composition percentages which is very flexible. When some rare CO2 eating trees came to be more frequent. But if that's true why can't plants change their composition again to adjust for human CO2-emissions pace?


Your question is a bit moot since the increases in CO2 did not come from burning trees or volcanoes and did not disappear because plants adapted.



Jeremy Shakun, et al., "Global warming preceded by increasing carbon dioxide concentrations during the last deglaciation," Nature 484.7392 (2012): 49-54.