I don't use toothpaste, haven't for over 10 years now, and my 11 year old son doesn't either.
Anti-bacterial ones are very bad for the "flora" of the mouth and gut.
A good way to help teeth stay strong and solid is to fast for as long as possible each day, eg. break-your-fast at lunchtime, or not eat an evening meal. This may be hard for people who are addicted to wheat/gluten, dairy/casein, or sugar/sucrose, and have to have their morning dose of cereal/toast and milk, yoghurt, etc in order to function, like an alcoholic needs their "hair of the dog", but it is definitely a good idea for the whole body because it gives it the time it needs in a non-acidic state to repair/maintain body tissues including bones and teeth ( eating anything, other than fruit, puts the body into an acidic state for several hours afterwards, during which time the body takes calcium from bones and teeth in order to restore the acid-alkali balance ).
Completely cutting out sugar/sucrose ( and cutting down on carbohydrates generally ) is also a good idea.
The most important reason to brush is to stimulate blood supply to the gums ( avoid gum disease ), but you can also achieve the same effect by eating lots of chewy/crunchy raw or flash-cooked vegetables, nuts, seeds, salad, etc, and flossing when necessary.
.