Dear Nice to Everyone,
I can tell this co-worker's behavior really bothers you.
There are several reasons why someone may ignore you or act in ways you define as rude. The person may be having a bad day, be totally consumed with their own thoughts and not even be aware of their behavior towards you. Or,they may be shy and anxious and afraid to talk to you. They may even have a crush on you.
What I am struck by is your conclusion that the person doesn't like you, and your interest in trying to figure out why that is the case. Your assumption may not be true.
Whenever we try to attribute someone else's behavior to something we said or did, we are going down a slippery slope. We are not in charge of anyone else's behavior, only are own. We have absolutely no control over what other people think, say or do. So to try and determine our own behavior based on other's reactions, is futile.
I am not saying you are definitely wrong. This co-worker may, in fact, not like you. However, that still doesn't mean you did anything in particular to cause him or her to feel that way. Maybe you have red hair and that reminds them of someone in their past who also had red hair, who they didn't happen to like.
The truth is, everyone has the right to not like every person they meet. Conversely, everyone also has the right to be human (not perfect) and to not be liked by everyone they know/work with.