Such an attitude is more likely to cause problems than to solve them. As people become more prone to expressing their animosity with gunfire (such as in the Mark Hummels tragedy), having a "you gotta stick up for yourself" mentality can lead to violence, rather than avoid it. I prosecuted a disorderly conduct/threats case once in which the defendant claimed that, as a trained martial artist, he felt justified in telling a store loss-prevention officer, "if you don't get away from me, I'm going to f**king kill you." This, he claimed, was a response to concern about the person following him in a crowded store.
If you are concerned for your safety, do not seek a confrontation with the person(s). Seek safety and assistance. Engaging an unknown assailant -- even verbally -- should be a last resort, because you do not know how that person is armed, trained, or influenced by drugs or alcohol. Sure, it may sting your pride to "back down," but that sting hurts less than a bullet.