You are misusing logic. If we went by that standard, nothing would be responsible for anything.
It is reasonable to assume that thousands of head-on collisions would damage the brain. Even one car crash can cause lifelong tissue damage; imagine what hundreds or thousands do.
That stipulated, you look for evidence. No-one had actually looked before, not really; we're sociologically prone to not look, because we like football. It's like asking people to look for brain damage caused by kneeling to pray to God, and I don't think that's too extreme a comparison.
Evidence was looked for, and found in abundance. Football players who received such shocks to the brain show, post-mortem, significant damage to the tissues. Live players who submit to tests show similar damage to their living brains. Such damage is not normally found in people who do not receive shocks to the brain for a living. It is found in those who do.
At this point, this is a done deal. Throwing people around and suddenly slamming them to a stop causes brain damage resulting in reduced capacity, depression, strange behavior, and eventually, for some, death by repeated trauma.
Now. What do we do about it? Football, American style, is crippling and killing the players. Do we stop? If not, why not? How far does the human delusion go in the face of reality?