> According to that logic, burning fossil fuels also is not harmful for the environment, because the CO2 eventually gets consumed by plants.

No, the difference in logic is based on the source of the CO2. Fossile fuels are burried in the ground and are not part of the carbon cycle. By removing them from the ground, we are adding new carbon to the carbon cycle rather. Coversely, if you burn wood, that carbon was (mostly) going to end back up in the carbon cycle and you've just sped up it's cycle and increased the portion of the cycling carbon that is in the atmosphere.

There are changes we can make to the cycle that do affect global warming (cutting down all the forests and killing all the kelp would greatly decrease the capacity of the cycle). Conversely, we can expand the carbon cycle by planting trees (that actually survive and form forests.)

However, you can't fix global warming by expanding the carbon cycle because you can't scale the natural cycle to match all the new carbon that is being added to it by buring fossile fuels. There are only two solutions, adding less carbon to the cycle by burning fewer fossile fuels and finding ways to remove carbon from the cycle by sequeresting it in long term ways.

Carbon taxes can fail to actually cause change if they allow fossil fuel burning to be offset by temporary bumps to the carbons cycle capacity because this doesn't really solve the problem and at best slightly delay it.

Cow "farts" (actually burps) are kinda the opposite, the methane is already part of the carbon cycle. However methane is a way more potent greenhouse gas than CO2 so by increasing amount of carbon cycle that is amospheric methane you are accelerating global warming until the methane decays into CO2.