I think you should challenge your beliefs on the statement "plants are carbon neutral", because there might only be two scenarios in which you are right that planting something and planting nothing has no difference:
1.) If you plant a commercial forest and then cut it down and burn it entirely.
2.) In the cosmic sense that all atoms will return to dust at some point.
In all other scenarios the statement is not helpful in particular because:
1.) Climate change is happening right now and is an acute global crisis which requires extremely short term measures (on an geological time scales). Growing a forest right now, captures carbon now when we need it most.
2.) If you cut down the trees after some time, you can actually just stack the trunks and they will most likely just be inert for a long time. The number of fungi and beetles that are specialized in dealing with decomposing wood is surprisingly low. In comparison to Carbon Capture technologies, which try to capture carbon from air and then store that somewhere, using trees is extremely easy.