Why do I care so much that someone who adds no value to my life at all doesn't like me?

Human beings are generally social which often drives us to build and maintain relationships with others. We are taught to "treat others as you would like to be treated" and are taught interpersonal effectiveness skills as we grow up to assist us with building healthy relationships.

Even though we "know" not everyone in life likes one another and sometimes someone can not like you for no apparent reason, it is a natural response to be bothered by it. If you feel generally liked by others, being unliked by someone with no explanation feels strange and uncomfortable.

A way to cope and reduce feeling bothered would be to shift your focus from "why am I so bothered" to "I accept how they feel and realize it does not determine my day". The uncertainty of why they are behaving the way that they are may actually be the bothersome factor opposed to being bothered that they do not like you. Their behavior does not make sense to you so it presents itself as a problem to be solved. When you accept that it is not a problem to be solved since it is out of your control and a situation to accept and move forward in a way that makes you more comfortable the bothersome feeling will reduce.

Taking inventory on if their behaviors actually impact your day or if it is your reaction to their behaviors that impacts your day is a great place to start. Using the rule of 5 when you notice that you are getting upset can help reduce the emotional charge. For the rule of 5 you would start by asking yourself: "Will this matter in 5 minutes? In 5 hours? In 5 days? In 5 weeks? In 5 Months? In 5 years?" As you go down the list you can better determine if your emotional charge matches how long the situation will actually impact you. 

Reminding yourself that they are a colleague, who you only see at work which is a determined window of time limiting their influence over your life, is another way to keep the situation in perspective. Distress tolerance skills can be useful as well, especially with reducing the emotional charge from any tense interactions before going home so that you have boundaries with what is going on and it does not seep into other areas of your life.