Not a teacher.
"Tackle" comes from American football. Each play in football ends when the player in possession of the ball is "tackled." You tackle someone by using your arms and body to force the ball-carrier to the ground. You literally throw your body into that of the other player in order to bring him to the ground.
By metaphor, to tackle something is to throw your entire being, your entire effort into the endeavour. It is also a victory for you when you tackle something or someone successfully.
So I doubt the people in question were pouncing on some beef. More likely they were eating it with much enthusiasm. Your other examples are likewise metaphorical.
Except for the thief. Reading this, I would assume that someone or ones physically stopped the thief by tackling him as you would a football player.
The only other oddball is the one about the horse. This is a different word "tackle." It means the equipment or gear that one would put on a horse. (It's also used by fishermen, who carry their stuff in a "tackle box.") It's a different word, except for being spelled and pronounced the same.