Trees should not be considered a renewable resource. It's true that if you cut a tree in a forest, another tree will grow in its place (or surrounding trees will grow bigger) without any additional energy or water needing to be expended by humans. That's why some people consider trees renewable.
There is one aspect that's often forgotten: time.
In order to avoid some of the catastrophic effects of climate warming, the IPCC urges to keep global warming below 1.5° C of pre-industrial levels. This can be achieved, it estimates with a 66% probability, by not emitting more than 420 GtCO2-equivalents (CO2e) until 2050 (based on the year 2018) and thereafter having net zero emissions. This figure refers to net emissions (emissions minus sequestration). Today, the world emits around 50 GtCO2e per year, and 60% of that is not sequestered (i.e. net). If you do the math, you realize that if we continued business as usual, we would already reach the IPCC budget by 2032.
It's crucial, then, to reduce emissions as quickly as possible. Today, not tomorrow. Or, expressed more plainly, we need to quit dicking around.
You probably know that plants perform photosynthesis, a process in which they convert light energy from the sun to a stored form of chemical energy. During this process, they extract CO2 from the atmosphere and save the C (carbon) for later use. The older a tree is, the more CO2 it sequesters from the atmosphere. While a typical sapling might extract around 5kg of CO2 per year, a ten year-old tree will already extract 22kg CO2. Trees take a long time to grow.
The most extreme example is Sequoiadendron giganteum, better known as Giant Sequoia. They truly are giants; it's not uncommon for them to grow 80 m tall and 6 m wide. They are considered the oldest living things on our planet, getting hundreds and thousands of years old. The oldest one, called Muir Snag, is located in the Sierra Navada mountain range of California and is thought to be more than 3,500 years old.
Trees not only extract CO2 from the atmosphere, they also store it. When a tree is cut down and burned as a so-called "renewable" energy source, or processed into timber, it releases CO2 back into the atmosphere. Which is not good.
People that label trees as renewable will argue that another tree will grow in its place and re-sequester the CO2 that was emitted by cutting down the previous tree. That, therefore, trees are a CO2-neutral resource. If you consider long time spans, this is true. This is also true for coal and oil - eventually the CO2 we release by burning oil and gas might also end up in the ground again.
Again, the problem is, time. If you cut and burn a tree today, it will release CO2 into the atmosphere today. It will take decades or centuries for other plants to sequester that carbon dioxide back from the atmosphere.
We don't have centuries. We can't put more than 420 GtCO2e into the atmosphere in the next 28 years.
We have to make sure that our trees, forests and ecosystems remain intact and reduce the land area we use for other things so that they can grow and sequester more carbon. This is the only known and scalable way to remove CO2 from the atmosphere and keep it there. Let's quit dicking around.