You don't need to be stronger, or a better fighter, you just need to make fighting you painful enough that the pain outweighs the gain. This is one of the key principles of deterrence (even on an international scale) -- you don't need to be strong enough to win the fight, you just have to be strong/vicious enough to inflict enough pain that "not fighting" becomes a better option for your opponent.
Or he'll "pick on you" with a huge stick out of kicking range, or he'll guard his nuts next time he's got you in a headlock.
Which weakens the headlock and leaves something else vulnerable (unless he's got three arms).
See, but that's the crux of the entire issue, and you (nor the OP) have not offered statistics backing this up. Anecdotes are not data, so I don't care if this "worked for me" or whatever.
A bully who gets his ass kicked, or doesn't win soundly enough, could easily escalate the next encounter with a knife or bat or something worse. Or maybe not! I don't know, neither do you or the OP, and so maybe we should not be making authoritative declarations about these things without consulting actual research.
Not true. Bullies tend to pick on people who won't fight back* because they're easy prey. If you demonstrate, even by losing, that you're not willing to take it from them anymore and that you will resist, you are no longer easy prey.
*Obviously this isn't true 100% of the time, but more often than not.