I've been training myself not to do this for years but it still takes incredible effort. Perhaps the most politically correct way to express this phenomenon is that it is a very common trait in people with AS, so much so that it is commonly associated with AS. Of course this trait is not strictly limited to people on the spectrum and NTs might do it as well, but it's FAR less common in the general population than for us aspies, and our doing it so commonly does seem to be related to our AS.
I like how you express how it "hurts" your ears to hear these mistakes. I feel the same way. However, it doesn't sound that way to NTs. It sounds like we're trying to show off how smart we are, or make the other person feel bad for making mistakes. Even if we explain that we don't mean it that way, that doesn't change how it feels for them. One of my closest friends regularly gets annoyed at me for being "pedantic" because I try to help him with his grammar (he's an English teacher after all) or his Czech (he's been living in the country for twice as long as me and can hardly speak a word). In my mind, I'm trying to help him, as well as myself because it annoys me to hear these mistakes repeated over and over again. In his mind, grammar is not an easy thing to deal with and remember, and I'm criticizing him for not being perfect.
It's probably similar to how we get criticized for not looking someone in the eye, or for talking too much, etc. For them it's really easy, but for us it's really difficult. They criticize us because it seems we're either intentionally doing something uncomfortable for them, or else we're too lazy to try to fix it. In reality, it's really hard for us and it can be devastating to work so hard at something and still get such a negative reaction. Try to think of it this way when you hear these mistakes, and it might help you be more patient in the future.