I was looking for an answer to this question for a long time but didn't find any.
why is communication skills used instead of communicative skills?
"Communicative skills" or "communicative abilities" can and does actually refer to the same concept as "communication skills". Here are some examples:
"Communication skills" is idiomatic. While it's more prevalent in general parlance, technical text does use "communicative skills".
Communication skills enable a person to be communicative.
The skills are not themselves communicative, that is, ready, able, and willing to communicate.