Do plants take in the same amount of CO2 as they release?
You've made one faulty assumption: that the second reaction is occuring at the same rate as the first.  In fact, plants only burn enough glucose to fuel their activities. Much of the formed glucose is converted into storage forms like cellulose and starch.  In fact, the vast majority of a plant's carbon mass comes ultimately from CO2 which has been converted photosynthetically into carbohydrate forms. (Further reading)

Ultimately, when plants die, those carbon molecules are used as food for other species, such as animal and bacteria.  Ultimately, whether in composted plant material or fecal mater, the carbon is deposited on the ground.  So ultimately it is correct that trees &amp; plants are removing CO2 permanently from the atmosphere.  Although some is being released to the atmosphere catabolically, more is re-absorbed for anabolic processes, and ultimately, that CO2 gets deposited on the ground in more complex carbon forms.