By Dixie 
You bring gifts. You compliment. You invite the person out for lunch. But the room immediately fills with ice the moment you step into the room. You are a nice person, right? But no matter what you do or say, this person seems to take offense or make small comments or gestures that look like friendship at the time, but later feel like a stab in the gut. The body language alone shows a smouldering dislike that goes way past indifference.
Maybe you will never be pinky-swear buddies, but is there any way to fix what little there is of this relationship? Should you even try?
Two action steps will determine that:
Search your head. Is there anything you have done or said that may have been misinterpreted (or interpreted correctly) as offensive? It should be something substantial, not a minor stupid comment which any human is guilty of on a daily basis. We all say and do idiotic things from time to time but any human over the age of 20 should give the other 99% of humanity a Get Out of Jail card for the small stuff, especially if it isn’t a pattern.
However…if you get that nagging feeling that wakes you up at 3 or 4am every night and digs heavily at your sleepy time, the problem is likely you. If this is the case, for your own sake as well as theirs, man up and go apologize. Do it one on one and be sincere, then don’t do it again. Over time and with proof that the offense isn’t repeated you will likely see some improvement. The relationship may or may not ever be BFF but at least the air will be cleared for tolerance and civility (ie, you may actually see the front side of this person sometimes instead of their back shoulder).
If you can’t find fault of your own, do a gut check as best you can of the other person. Is there some reason this person came into the relationship disliking you? Maybe someone else poisoned the well by bringing in assumptions, half truths and outright lies about your character and motives. Maybe you represent part of the past that this person wants desperately to forget or make disappear. Maybe this person is very insecure and somehow sees you as a threat or competition in some way.
If this is the problem, you are dealing with a losing situation. You can only control your own actions and reactions not theirs, and if there is no intent to resolve on their part there will be no positive movement. At least not for the foreseeable future. Just the facts, Ma’am.
You are welcome to try and clear up misconceptions, but don’t waste a lot of time or effort. Until this person sees a reason to be friends with you, the likelihood of them accepting any defensive gesture on your part is slim. As slim as a wallet on the 31st of the month.
What to do? Be nice but don’t pursue. Be friendly, but distant. Expect the same behavior to continue but don’t allow it to impact how you feel about yourself. If you have done nothing horribly wrong, yet you have made gestures of friendship which were not accepted, it’s OK. Not everyone will like everyone on this side of Planet Earth. Accept reality and let it roll off your back like Daffy Duck taking a bath.
There are other fishy friends in the sea who will appreciate you. Pinky swear promise.