給 hands the thing to the receiver, who ends up holding it; 跟 sets a companion you act alongside, no thing changing hands. 我給他錢 (he gets the money) vs 我跟他走 (we move together).
給 points the thing toward the receiver who gets it; 向 only aims the action at a target without delivering anything. 給他 = he receives; 向他 = facing him.
thing before receiver: 他給一本書我 → 他給我一本書
borrowing 跟 for the receiver: 他跟我一本書 → 他給我一本書
dropping the receiver when one is meant: 他給一本書 → 他給我一本書
English needs 'to' before the receiver (give a book to me); learners insert a word or flip the order, where 給 already carries the to-the-receiver direction and the receiver comes first.