Older trees fix less carbon than newer trees. Paper products are essentially made of carbon extracted from the air, and you just plant new trees in the farm afterwards.
Plastic, on the other hand, is taking carbon that's already sequestered deep underground and pulling it to the surface, with an obvious net positive carbon footprint.
All that said, as far as I remember, trees are not and can not be a very major form of carbon capturing due to the available area in the globe and the amount of excess carbon we need to get rid of.
You're twisting my words. Trees can't be the solution to our carbon problem, because they have no way to compete with humanity burning millions of years of carbon storage as fuel.
That doesn't mean trees aren't extremely important in countless different ways.
Which also doesn't mean that we shouldn't use wood as a material, if it's produced with principles.
Timber industries have shown for centuries they aren't concerned with carbon capture of forests and actively try to monoculture "regenerating" forests with herbicides which drastically reduces carbon capture.
This documentary gives a good idea into my reasoning on why believing timber propaganda that "trees are better when cut down and regrowing" is false:
Plastic, on the other hand, is taking carbon that's already sequestered deep underground and pulling it to the surface, with an obvious net positive carbon footprint.
All that said, as far as I remember, trees are not and can not be a very major form of carbon capturing due to the available area in the globe and the amount of excess carbon we need to get rid of.