Students who actually do go the extra mile and show their essay to a teacher before sending it often go straight to their favorite teacher, or at least one who likes them a lot. That’s natural, but if that person is your favorite teacher, then he/she probably likes you, too, and may be likely to pat you on the back and tell you what you want to hear rather than give you the honest feedback your essay needs to improve. This isn’t always the case, but it can be, especially with that teacher who seems to want to be good buddies with lots of the students (every school has one). On the other hand, a teacher who doesn’t know you (and especially one who does know you and isn’t particularly fond of you) doesn’t have any reason to lie to you about your essay’s shortcomings. In fact, a teacher who doesn’t like you may enjoy the opportunity to criticize you. You might as well let him/her do so in a way that helps you out – you could get some very useful feedback from the process. Plus, as an aside, you’ll probably earn some respect from that teacher as well. If you know he/she doesn’t like you and you still go ask for his/her expertise, that shows guts.
NOTE: I know some of you reading this are thinking something like, “Gosh, I know all the teachers, and I can’t even think of ONE teacher who doesn’t like me. They all like me!” If that’s the case, then – well, good for you. Keep in touch with as many of them as you can for future recommendation letters and references!