Let me make it extremely simple: there are future expected doublings of CO2 ppm, but there are none for CH4. The share of warming for CH4 compared to CO2 is low and will only get lower.
So, you're right that CO2 is growing a bit faster, but the difference really is rather small.
In addition to this, there are highly nonlinear effects that may occur in the future that others have alluded to, such as the clathrate gun hypothesis [3]. Even in the absence of such dramatic effects, you would expect methane levels to further increase with increasing meat consumption in countries that are getting wealthier (e.g. in India, China).
Edit: I should also point out that the claim that only future doublings in CO2 concentration matter is totally wrong. Even in the IPCC report's worst case scenario, CO2 concentrations will grow to ca. 1000 ppm by 2100, just over a single further doubling [4]. In the best case scenario, they stabilize a bit under 500 ppm, which is just another 20% increase from today. In that best case scenario (B1), global temperatures are still expected to rise by slightly more than 1.5°C by 2100 [5]!
[1] https://www.esrl.noaa.gov/gmd/ccgg/trends_ch4/
[2] https://www.esrl.noaa.gov/gmd/ccgg/trends/
[3] https://en.wikipedia.org/wiki/Clathrate_gun_hypothesis
[4] https://en.wikipedia.org/wiki/File:Projected_changes_over_th...
[5] https://www.ipcc.ch/site/assets/uploads/2018/02/ar4-wg1-chap... (Fig. 10.4)
CO2 is growing exponentially.
Meaningful, yes. Exponential, not hardly.