Seems he is more pissed off at the kindergartener who "scribbles with crayons" to show support of his "buddies".Any reasonable reading of that passage does not lead one to think Tillman is pissed off with children, rather than the people who made the decisions that ensured they spent the precious first years of their life interacting with their dads via drawings.
Excuse me what are you reading? Here's the paragraph again.
Somehow back at home, support for the soldiers meant having a five-year-old kindergartener scribble a picture with crayons and send it overseas, or slapping stickers on cars, or lobbying Congress for an extra pad in a helmet. It's interesting that a soldier on his third or fourth tour should care about a drawing from a five-year-old; or a faded sticker on a car as his friends die around him; or an extra pad in a helmet, as if it will protect him when an IED throws his vehicle 50 feet into the air as his body comes apart and his skin melts to the seat
It's obvious that kindergarteners support of the troops is a subject of Mr. Tillman's poisonous pen. He is mocking their support of the troops and of him.