Are There Really Too Many People?
We share the planet with 5.7 billion people. If one could stand all the people in the world, men, women and children two feet apart, how much of the world would they take up? All of Africa? All of North America? New York state? If every person alive today stood two feet apart they would fill less than the area of Dallas County! And there would still be room for all the buildings! If the world's people were put together into families of four living on 50' by 100' lots, they could all live in the state of Texas, with more than seven thousand square miles left over. So the total number of people is not the real problem, at least at this point.
Therein lies the problem -- no forward thinking. You are looking at the world where it is right now. But you are not looking at where the world is going.
OK lets look forward
If world population tops out at 12 billion eventually, then each person could have 608½ sq ft in Texas (more space then many New York apartments)
Back to the tree, cutting a few branches is not going to harm anything; heck Mother Nature does it all the time. A month ago I had a tree come down in a wind storm, the world did not end over it. But I do have a lot more campfire wood.